Results for “merit function” — Page 7

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Uncrewed Lunar Surface Operations and Support Activities

Sustained human presence on the surface of the Moon and future missions to Mars require increased independence from surface crews and Earth-based mission control to operate efficiently, safely, and reliably. The time for surface crews to perform tasks will be limited. Extravehicular activities by surface personnel are burdensome and time-consuming, even when a continuous human presence on the surface occurs. Identifying and balancing human/automation roles and tasks and infusing automation and autonomy practices early in a system’s lifecycle will be essential to achieve mission objectives. Among these objectives are attaining a sustained human presence, improving performance and mission effectiveness, reducing operations and maintenance (O&M) costs, and ensuring operations that are robust to communication delays. To achieve these objectives, an operational shift toward increased automation and autonomy with less reliance on humans is needed. Uncrewed lunar surface operations and support activities occur when surface crews are not present or are independent of surface crew timeline activities requiring no surface crew oversight or intervention. These uncrewed surface opportunities can also be planned to minimize crew workload that avoids routine maintenance and support tasks, thus maximizing crew exploration time. Uncrewed preparations such as staging and prepositioning equipment and materials before the crew arrives could improve crew task efficiency. Additional opportunities exist to conduct uncrewed science, exploration, and utilization. Uncrewed surface architecture functions can include science and exploration; habitation; launch and landing support; surface communication and navigation; surface power generation and distribution; human surface mobility; lifting, handling, manipulating; excavation, construction, and site preparation; logistics management; maintenance and repair; surface resource utilization; integrated site operations and shared support services (e.g., site scheduling/prioritization, dust mitigation/contamination control, and surface safety). Early robotic lunar surface campaigns will provide information on the availability of resources, such as oxygen and water, and demonstrate surface-based technologies. After the Artemis III human lunar return mission, a series of landers will deliver surface systems, cargo, supplies, science packages, spare parts, and commodities. A balance of crewed and uncrewed surface operations will enable a sustained lunar surface presence at the South Pole of the Moon at a site that will be known as the Artemis Base Camp (ABC). It is envisioned that base camp operations on and around the Moon will then help prepare for the mission durations and activities needed to support the first human mission to Mars. Before long-duration crew missions to the base camp can occur, the necessary surface infrastructure will be pre-deployed and verified operational. Surface assets will be teleoperated and remotely managed from Earth. Additionally, robotic and short-duration crewed missions to the ABC will ensure the site’s merit to achieve long-term science objectives, availability of usable resources, and that terrain, seasonal variations, and illumination conditions are acceptable. ABC will consist of different areas where specific functions and services are rendered, including: • Launch and Landing Area • Habitation Area • Power Production Area • Resource Areas Launch and Landing Area—The launch and landing area will support associated functions for the arrival and departure of vehicles, such as crewed landing and ascent and uncrewed cargo deliveries and offloading. It will evolve from an unimproved site at the beginning of the exploration campaign to a more sustainable landing and launch area that can support repeated arrivals and departures. Initial uncrewed Lunar Terrain Vehicle (LTV) surface operations may include emplacement of navigation beacons and communication equipment, real-time video and photography of landing/liftoff events, and element repositioning, such as portable utility power (PUP) (applicable for other landed assets at other areas). Site preparations, such as surface leveling, soil compaction, and berm/path construction, may be needed for a more sustainable launch and landing area capable of accommodating vehicles that are increasingly more reusable and reduce the effects of plume surface interactions and ejecta impacts on nearby surface assets. During the ABC missions, cargo and logistics will be delivered to the lunar surface via robotic cargo landers before the crew arrives. These shipments, which can arrive in pressurized logistics carriers, will deliver the logistics necessary to support a crewed mission and include items such as food, water, equipment spares, etc. Providing the capability to retrieve, offload, and transport the logistics closer to the ABC site before the arrival of the crew will increase the overall efficiency of crew operations once they arrive. In the sustained phase of exploration, other supporting services may be needed, such as lander propellant servicing, surface power services, commodity refreshes, and additional inspection, maintenance, and repair capabilities, to sustain a cadence of extended personnel stays and cargo arrivals and departures. Habitation Area—Uncrewed support to surface habitation could involve supporting activation and pre-entry operations of the habitat while the crew is in orbit at the Gateway outpost preparing for a surface landing. Surface Habitat (SH) uncrewed operations may include bringing the cabin environment to a habitable temperature and air mix and activating other critical crew support systems. Potential crop production uncrewed tasks in the SH could also include autonomous watering and tending. Additionally, when the crew departs, the SH enters dormancy for the long period of uncrewed operation. A logistical staging area could also be collocated near the SH. If so, staging operations for crew supplies, waste re-location, and recycling operations may be opportunities for uncrewed operations. Power Production Area—The Fission Surface Power (FSP) element and its supporting distribution equipment provide power to surface elements as needed across the ABC to supplement day-to-day operations and survive lunar nights. Uncrewed support of this power system includes any initial LTV-assisted deployments of cables and other distributed equipment, associated electrical connections, and system testing and activation operations. Robotically performing some inspections, maintenance, or repair tasks on the power distribution equipment could reduce the surface crew workload. Resource Area— Uncrewed resource prospecting, mapping, and characterizing possible resource sites is likely to be time-consuming and represents an opportunity for uncrewed operations between crewed missions. Uncrewed mobile equipment operations will be needed in the extreme environments of permanently shadowed locations where resource extractions occur. As In-Situ Resource Utilization (ISRU) pilot plant operations begin, uncrewed surface support activities with available mobile and portable assets (LTV, PUP, etc.) will better support these operations. Any produced commodities can be stored at a centralized storage location for future use. Also associated with these operations is the use of mobile robotic excavators for resource acquisition and robotic/autonomous regolith processing. The waste tailings generated during excavation and regolith processing would also need to be transported and deposited at a dedicated location. Surface assets will continue operating between crew visits to maintain surface capabilities, conduct lunar surface science, technology demonstrations, and public outreach opportunities. Additionally, certain sustaining tasks that would consume valuable crew time could be performed before crew arrival, or after their departure. This capability may offer more affordable options to construct, activate, test, and maintain a broad set of surface assets. Telerobotically operated human surface mobility systems, such as the LTV and Pressurized Rover (PR), can be utilized for various tasks. Surface environmental conditions pose a distinct challenge for all these activities. Surface illumination and localized shadows are one such factor. Night-survival operations could consist of thermal management, battery pre-charging, and load shedding. Some surface systems may hibernate through the night and then awake and continue nominal operations. Uncrewed mobile assets may use a more adaptive approach to optimize their power and operations; one method is to follow the sunlight. Night-survival operations may be initiated remotely by teleoperation, automated, or accomplished by supervised autonomous operation. The ability to pre-deploy and control remote assets in orbit or on Mars before the arrival of the mission crew is a key capability that can be simulated on the moon. The base camp provides a venue where these advanced operational concepts, technologies, and autonomous methods and techniques, including the incorporation of time delays to simulate Earth-Mars latency can be replicated to help buy down future Mars mission risks. This paper will examine the evolution of uncrewed lunar surface operations and support activities. It will also discuss the lunar surface environmental conditions (thermal, lighting, terrain, topography, communications) along with the challenges they pose on uncrewed surface operations, and the performance of these activities with limited to minimal human interaction and/or teleoperation. Since lunar missions include Mars mission analogs, such investigation provides the framework for future uncrewed Mars mission support.

Mark E Lewis↗

NASA NTRS1993

Design optimization of high-speed proprotor aircraft

NASA's high-speed rotorcraft (HSRC) studies have the objective of investigating technology for vehicles that have both low downwash velocities and forward flight speed capability of up to 450 knots. This paper investigates a tilt rotor, a tilt wing, and a folding tilt rotor designed for a civil transport mission. Baseline aircraft models using current technology are developed for each configuration using a vertical/short takeoff and landing (V/STOL) aircraft design synthesis computer program to generate converged vehicle designs. Sensitivity studies and numerical optimization are used to illustrate each configuration's key design tradeoffs and constraints. Minimization of the gross takeoff weight is used as the optimization objective function. Several advanced technologies are chosen, and their relative impact on future configurational development is discussed. Finally, the impact of maximum cruise speed on vehicle figures of merit (gross weight, productivity, and direct operating cost) is analyzed. The three most important conclusions from the study are payload ratios for these aircraft will be commensurate with current fixed-wing commuter aircraft; future tilt rotors and tilt wings will be significantly lighter, more productive, and cheaper than competing folding tilt rotors; and the most promising technologies are an advanced-technology proprotor for both tilt rotor and tilt wing and advanced structural materials for the folding tilt rotor.

Schleicher, David R.↗

NASA NTRS2018

Diagnostic for Verifying the Thrust Vector Requirement of the AEPS Hall-Effect Thruster and Comparison to the NEXT-C Thrust Vector Diagnostic

A diagnostic has been designed and fabricated to verify the thrust vector requirement for the Advanced Electric Propulsion System (AEPS) Hall Effect Rocket with Magnetic Shielding (HERMeS) thruster. This diagnostic will be used to verify that the propulsion system thrust vector offset from the mounting surface normal vector does not exceed 1.5 degrees over the entire throttling range and over the course of 23,000 hours of thruster testing. The diagnostic will also not violate the thruster's required voltage standoff capability in the presence of carbon backsputter by being minimally intrusive and not significantly adding to the facility backsputtered rate. Based on these requirements, an appropriate diagnostic design was determined to comprise of an array of 23 Faraday probes swept through the plume in an arc 1m from the thruster to map the beam current density. The beam current density centroid of the plume is assumed to track the thrust vector within an acceptable level of uncertainty. Additionally, a reference system, including optical alignment to the mounting surface normal vector and tilt sensors, was devised to periodically calibrate the probe position and motion throughout the long duration wear test campaign. Initial measurements of the thruster plume have been acquired to demonstrate the diagnostics functionality, verify procedures, and assess any necessary improvements prior to implementation of the diagnostic during the AEPS Engineering Development Unit (EDU) long duration wear test. To illustrate the merits of differing approaches to thrust vector determination for different classes of electric propulsion thrusters, NASA's Evolutionary Xenon Thruster-Commercial (NEXT-C) thrust vector diagnostic design details and recent data are also discussed (Appendix A).

Benavides, Gabriel F.↗

NASA NTRS2018

Diagnostic for Verifying the Thrust Vector Requirement of the AEPS Hall-Effect Thruster and Comparison to the NEXT-C Thrust Vector Diagnostic

A diagnostic has been designed and fabricated to verify the thrust vector requirement for the Advanced Electric Propulsion System (AEPS) Hall Effect Rocket with Magnetic Shielding (HERMeS) thruster. This diagnostic will be used to verify that the propulsion system thrust vector offset from the mounting surface normal vector does not exceed 1.5 degrees over the entire throttling range and over the course of 23,000 hours of thruster testing. The diagnostic will also not violate the thruster's required voltage standoff capability in the presence of carbon backsputter by being minimally intrusive and not significantly adding to the facility backsputtered rate. Based on these requirements, an appropriate diagnostic design was determined to comprise of an array of 23 Faraday probes swept through the plume in an arc 1m from the thruster to map the beam current density. The beam current density centroid of the plume is assumed to track the thrust vector within an acceptable level of uncertainty. Additionally, a reference system, including optical alignment to the mounting surface normal vector and tilt sensors, was devised to periodically calibrate the probe position and motion throughout the long duration wear test campaign. Initial measurements of the thruster plume have been acquired to demonstrate the diagnostics functionality, verify procedures, and assess any necessary improvements prior to implementation of the diagnostic during the AEPS Engineering Development Unit (EDU) long duration wear test. To illustrate the merits of differing approaches to thrust vector determination for different classes of electric propulsion thrusters, NASA's Evolutionary Xenon Thruster-Commercial (NEXT-C) thrust vector diagnostic design details and recent data are also discussed (Appendix A).

Benavides, Gabriel F.↗

NASA NTRS2018

Diagnostic for Verifying the Thrust Vector Requirement of the AEPS Hall-Effect Thruster and Comparison to the NEXT-C Thrust Vector Diagnostic

A diagnostic has been designed and fabricated to verify the thrust vector requirement for the Advanced Electric Propulsion System (AEPS) Hall Effect Rocket with Magnetic Shielding (HERMeS) thruster. This diagnostic will be used to verify that the propulsion system thrust vector offset from the mounting surface normal vector does not exceed 1.5 degrees over the entire throttling range and over the course of 23,000 hours of thruster testing. The diagnostic will also not violate the thruster's required voltage standoff capability in the presence of carbon backsputter by being minimally intrusive and not significantly adding to the facility backsputtered rate. Based on these requirements, an appropriate diagnostic design was determined to comprise of an array of 23 Faraday probes swept through the plume in an arc 1m from the thruster to map the beam current density. The beam current density centroid of the plume is assumed to track the thrust vector within an acceptable level of uncertainty. Additionally, a reference system, including optical alignment to the mounting surface normal vector and tilt sensors, was devised to periodically calibrate the probe position and motion throughout the long duration wear test campaign. Initial measurements of the thruster plume have been acquired to demonstrate the diagnostics functionality, verify procedures, and assess any necessary improvements prior to implementation of the diagnostic during the AEPS Engineering Development Unit (EDU) long duration wear test. To illustrate the merits of differing approaches to thrust vector determination for different classes of electric propulsion thrusters, NASA's Evolutionary Xenon Thruster-Commercial (NEXT-C) thrust vector diagnostic design details and recent data are also discussed (Appendix A).

Advanced Electric Propulsion System (AEPS)↗

NASA NTRS2018

Space Science and Technology Partnership Forum: Analysis for a Joint Demonstration of High Priority, In-Space Assembly Technology

The various U. S. government agencies that are pursuing in-space assembly technology have a common need to demonstrate technological capabilities on a space-based platform. Several of the agencies, and different mission developers within an agency, have independently begun planning such demonstrations. This paper reports on a study of how well the different planned platforms could support demonstrations of the agencies’ joint needs. The study first prioritized a comprehensive list of the needs for in-space assembly capabilities across the agencies against jointly agreed evaluation criteria. Each planned demonstration platform was characterized to a first order. The capability needs were qualitatively assessed against four figures of merit including their joint priority, and the platforms were assessed against five criteria to produce a quantitative weighting factor of reach capability need and each platform. A Quality Function Deployment (QFD) matrix was used to deploy the weighted capability needs against the weighted platforms capabilities. This first-order assessment showed that the platforms reflect a great deal of redundant capability without a strong reason to prefer one over the others. These results were largely insensitive to the details of the assumptions.

Hamill, Doris L↗

NASA NTRS1982

Space Applications of Automation, Robotics and Machine Intelligence Systems (ARAMIS). Volume 1: Executive Summary

Potential applications of automation, robotics, and machine intelligence systems (ARAMIS) to space activities, and to their related ground support functions are explored. The specific tasks which will be required by future space projects are identified. ARAMIS options which are candidates for those space project tasks and the relative merits of these options are defined and evaluated. Promising applications of ARAMIS and specific areas for further research are identified. The ARAMIS options defined and researched by the study group span the range from fully human to fully machine, including a number of intermediate options (e.g., humans assisted by computers, and various levels of teleoperation). By including this spectrum, the study searches for the optimum mix of humans and machines for space project tasks.

Miller, R. H.↗

NASA NTRS1996

Support of Helicopter 'Free Flight' Operations in the 1996 Olympics

The microcosm of activity surrounding the 1996 Olympic Games provided researchers an opportunity for demonstrating state-of-the art technology in the first large-scale deployment of a prototype digital communication/navigation/surveillance system in a confined environment. At the same time it provided an ideal opportunity for transportation officials to showcase the merits of an integrated transportation system in meeting the operational needs to transport time sensitive goods and provide public safety services under real-world conditions. Five aeronautical CNS functions using a digital datalink system were chosen for operational flight testing onboard 91 aircraft, most of them helicopters, participating in the Atlanta Short-Haul Transportation System. These included: GPS-based Automatic Dependent Surveillance, Cockpit Display of Traffic Information, Controller-Pilot Communications, Graphical Weather Information (uplink), and Automated Electronic Pilot Reporting (downlink). Atlanta provided the first opportunity to demonstrate, in an actual operating environment, key datalink functions which would enhance flight safety and situational awareness for the pilot and supplement conventional air traffic control. The knowledge gained from such a large-scale deployment will help system designers in development of a national infrastructure where aircraft would have the ability to navigate autonomously.

Branstetter, James R.↗

NASA NTRS1990

Sensor performance analysis

The theory is described and the equations required to design are developed and the performance of electro-optical sensor systems that operate from the visible through the thermal infrared spectral regions are analyzed. Methods to compute essential optical and detector parameters, signal-to-noise ratio, MTF, and figures of merit such as NE delta rho and NE delta T are developed. A set of atmospheric tables are provided to determine scene radiance in the visible spectral region. The Planck function is used to determine radiance in the infrared. The equations developed were incorporated in a spreadsheet so that a wide variety of sensor studies can be rapidly and efficiently conducted.

Montgomery, H. E.↗

NASA NTRS2003

Standards-and Component-Based Mission Operations Architecture at NASA's Goddard Space Flight Center

NASA Goddard Space Flight Center (GSFC) manages many of NASA s earth and space science satellite missions. A wide variety of commercial products and GSFC-developed software components are typically integrated into a unique system configuration for each mission. Independent development of the many mission operations center systems has led to systems that are expensive to integrate, difficult to infuse with new capabilities developed for other programs, and cumbersome to maintain. This traditional approach becomes even more problematic as NASA moves towards satellite constellations, new operations concepts, and even further budgets reductions. The GSFC Mission Services Evolution Center (GMSEC) is creating a new architecture for future missions at GSFC. Instead of selecting the best-in-class components and creating a standard control center system, GMSEC is developing component interface standards so that multiple products can plug-and-play into the configuration. Missions can then select the best components based on the merits of the product and not simply based on recent integration history at NASA. The GMSEC system utilizes a publish/subscribe information bus and standard XML-based key message interfaces. Functional components can either match directly to the interface standard, or adapters can be developed to match the product's interface to the GMSEC standard with out impacting the source product. Applications Program Interfaces (API's) are being developed to isolate the underlying middleware from the applications software and to allow the middleware product to be switched if necessary. Interface Control Documents (ICDs) between each pair of communicating components is replaced by a single message/API specification document. New applications must simply match to the information bus standards and need not worry about all of the other applications in the system. For legacy software, adapters can be developed to facilitate communications between the application and the information bus. As the approach has matured, it has become apparent that it can provide innovative solutions to some of the multi-satellite challenges facing GSFC.

Smith, Danford↗

NASA NTRS2015

A Novel Approach for Engaging Academia in Collaborative Projects with NASA through the X-Hab Academic Innovation Challenge

The X-Hab Academic Innovation Challenge, currently in its sixth year of execution, provides university students with the opportunity to be on the forefront of innovation. The X-Hab Challenge, for short, is designed to engage and retain students in Science, Technology, Engineering and Math (STEM). NASA identifies necessary technologies and studies for deep space missions and invites universities from around the country to develop concepts, prototypes, and lessons learned that will help shape future space missions and awards seed funds to design and produce functional products of interest as proposed by university teams according to their interests and expertise. Universities propose on a variety of projects suggested by NASA and are then judged on technical merit, academic integration, leveraged funding, and outreach. The universities assemble a multi-discipline team of students and advisors that invest months working together, developing concepts, and frequently producing working prototypes. Not only are students able to gain quality experience, working real world problems that have the possibility to be implemented, but they work closely with subject matter experts from NASA who guide them through an official engineering development process.

Habitats↗

NASA NTRS2015

A Novel Approach for Engaging Academia in Collaborative Projects with NASA through the X-Hab Academic Innovation Challenge

The X-Hab Academic Innovation Challenge, currently in its sixth year of execution, provides university students with the opportunity to be on the forefront of innovation. The X-Hab Challenge, for short, is designed to engage and retain students in Science, Technology, Engineering and Math (STEM). NASA identifies necessary technologies and studies for deep space missions and invites universities from around the country to develop concepts, prototypes, and lessons learned that will help shape future space missions and awards seed funds to design and produce functional products of interest as proposed by university teams according to their interests and expertise. Universities propose on a variety of projects suggested by NASA and are then judged on technical merit, academic integration, leveraged funding, and outreach. The universities assemble a multi-discipline team of students and advisors that invest months working together, developing concepts, and frequently producing working prototypes. Not only are students able to gain quality experience, working real world problems that have the possibility of be implemented, but they work closely with subject matter experts from NASA who guide them through an official engineering development process.

X-Hab Challenge↗

NASA NTRS1992

Design of high speed proprotors using multiobjective optimization techniques

An integrated, multiobjective optimization procedure is developed for the design of high speed proprotors with the coupling of aerodynamic, dynamic, aeroelastic, and structural criteria. The objectives are to maximize propulsive efficiency in high speed cruise and rotor figure of merit in hover. Constraints are imposed on rotor blade aeroelastic stability in cruise and on total blade weight. Two different multiobjective formulation procedures, the Min summation of beta and the K-S function approaches are used to formulate the two-objective optimization problems.

Mccarthy, Thomas R.↗

NASA NTRS1998

Hard X-Ray and Wide Focusing Telescopes

Studies are being carried out to compare the performance of several different separation materials used in the replication process. This report presents the results obtained during the second year of a program which consists of replicating smooth, thin substrates, depositing multilayer coatings upon them, and evaluating their performance. Replication and multilayer coatings are both critically important to the development of focussing hard X-ray telescopes that function up to 100 keV. The activities of the current year include extending the comparison between sputtered amorphous carbon and evaporated gold to include sputtered as well as evaporated gold. The figure of merit being the smoothness of the replica which has a direct effect on the specular reflectivity. These results were obtained with epoxy replication, but they should be applicable to electroformed nickel, the process we expect to use for the ultimate replicated optics.

Gorenstein, Paul↗

NASA NTRS1982

Space applications of Automation, Robotics and Machine Intelligence Systems (ARAMIS). Volume 4: Application of ARAMIS capabilities to space project functional elements

Applications of automation, robotics, and machine intelligence systems (ARAMIS) to space activities and their related ground support functions are studied, so that informed decisions can be made on which aspects of ARAMIS to develop. The specific tasks which will be required by future space project tasks are identified and the relative merits of these options are evaluated. The ARAMIS options defined and researched span the range from fully human to fully machine, including a number of intermediate options (e.g., humans assisted by computers, and various levels of teleoperation). By including this spectrum, the study searches for the optimum mix of humans and machines for space project tasks.

Miller, R. H.↗

NASA NTRS1991

Impact of inertia, friction, and backlash upon force control in telemanipulation

The mechanical behavior of master controllers of telemanipulators has been a concern of both designers and implementors of telerobotic systems. In general, the literature recommends that telemanipulator systems be constructed that minimize inertia, friction, and backlash in an effort to improve telemanipulative performance. For the most part, these recommendations are founded upon theoretical analysis or simply intuition. Although these recommendations are not challenged on their merit, the material results are measured of building and fielding telemanipulators that possess less than ideal mechanical behaviors. Experiments are described in which forces in a mechanical system with human input are evaluated as a function of mechanical characteristics such as inertia, friction, and backlash. Results indicate that the ability of the human to maintain gripping forces was relatively unaffected by dynamic characteristics in the range studied, suggesting that telemanipulator design in this range should be based on task level force control requirements rather than human factors.

Duffie, Neil A.↗

NASA NTRS2010

Technology Assessment for Large Vertical-Lift Transport Tiltrotors

The technical community has identified rotor efficiency as a critical enabling technology for large vertical-lift transport (LVLT) rotorcraft. The size and performance of LVLT aircraft will be far beyond current aircraft capabilities, enabling a transformational change in cargo transport effectiveness. Two candidate approaches for achieving high efficiency were considered for LVLT applications: a variable-diameter tiltrotor (VDTR) and a variable-speed tiltrotor (VSTR); the former utilizes variable-rotor geometry and the latter utilizes variable-rotor speed. Conceptual aircraft designs were synthesized for the VDTR and VSTR and compared to a conventional tiltrotor (CTR). The aircraft were optimized to a common objective function and bounded by a set of physical- and requirements-driven constraints. The resulting aircraft were compared for weight, size, performance, handling qualities, and other attributes. These comparisons established a measure of the relative merits of the variable-diameter and -speed rotor systems as enabling technologies for LVLT capability.

Germanowski, Peter J.↗

NASA NTRS1987

Solutions of some problems in applied mathematics using MACSYMA

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Punjabi, Alkesh↗