Engineering topics

Roithmayr, Carlos M.

Publications and source records attributed to Roithmayr, Carlos M..

35 records · Page 2

NASA NTRS2009

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

Roithmayr, Carlos M.↗

NASA NTRS2007

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

Roithmayr, Carlos M.↗

NASA NTRS2005

Comet/Asteroid Protection System (CAPS): Preliminary Space-Based Concept and Study Results

There exists an infrequent, but significant hazard to life and property due to impacting asteroids and comets. There is currently no specific search for long-period comets, smaller near-Earth asteroids, or smaller short-period comets. These objects represent a threat with potentially little or no warning time using conventional ground-based telescopes. These planetary bodies also represent a significant resource for commercial exploitation, long-term sustained space exploration, and scientific research. The Comet/Asteroid Protection System (CAPS) is a future space-based system concept that provides permanent, continuous asteroid and comet monitoring, and rapid, controlled modification of the orbital trajectories of selected bodies. CAPS would expand the current detection effort to include long-period comets, as well as small asteroids and short-period comets capable of regional destruction. A space-based detection system, despite being more costly and complex than Earth-based initiatives, is the most promising way of expanding the range of detectable objects, and surveying the entire celestial sky on a regular basis. CAPS would provide an orbit modification system capable of diverting kilometer class objects, and modifying the orbits of smaller asteroids for impact defense and resource utilization. This Technical Memorandum provides a compilation of key related topics and analyses performed during the CAPS study, which was performed under the Revolutionary Aerospace Systems Concepts (RASC) program, and discusses technologies that could enable the implementation of this future system.

Mazanek, Daniel D.↗

NASA NTRS2005

Accurate Determination of Comet and Asteroid Orbits Leading to Collision With Earth

Movements of the celestial bodies in our solar system inspired Isaac Newton to work out his profound laws of gravitation and motion; with one or two notable exceptions, all of those objects move as Newton said they would. But normally harmonious orbital motion is accompanied by the risk of collision, which can be cataclysmic. The Earth s moon is thought to have been produced by such an event, and we recently witnessed magnificent bombardments of Jupiter by several pieces of what was once Comet Shoemaker-Levy 9. Other comets or asteroids may have met the Earth with such violence that dinosaurs and other forms of life became extinct; it is this possibility that causes us to ask how the human species might avoid a similar catastrophe, and the answer requires a thorough understanding of orbital motion. The two red square flags with black square centers displayed are internationally recognized as a warning of an impending hurricane. Mariners and coastal residents who know the meaning of this symbol and the signs evident in the sky and ocean can act in advance to try to protect lives and property; someone who is unfamiliar with the warning signs or chooses to ignore them is in much greater jeopardy. Although collisions between Earth and large comets or asteroids occur much less frequently than landfall of a hurricane, it is imperative that we learn to identify the harbingers of such collisions by careful examination of an object s path. An accurate determination of the orbit of a comet or asteroid is necessary in order to know if, when, and where on the Earth s surface a collision will occur. Generally speaking, the longer the warning time, the better the chance of being able to plan and execute action to prevent a collision. The more accurate the determination of an orbit, the less likely such action will be wasted effort or, what is worse, an effort that increases rather than decreases the probability of a collision. Conditions necessary for a collision to occur are discussed, and warning times for long-period comets and near-Earth asteroids are presented.

Roithmayr, Carlos M.↗

NASA NTRS2005

Keeping a Spacecraft on the Sun-Earth Line

Measurements of Earth's atmosphere as it occults sunlight can be obtained advantageously from a spacecraft placed in the proximity of the Sun-Earth Lagrange point L2. Maintaining the condition of continuous solar occultation by all parts of the atmospheric disk requires that the displacement of the spacecraft perpendicular to the Sun-Earth line remains less than 200 km. However, the gravitational force exerted by the Earth s moon must be negated by propulsion in order to meet this rather tight constraint. We provide an estimate of propulsive force needed to keep the spacecraft coincident with L2, as well as estimates of velocity increments needed to maintain various trajectories in the close vicinity of L2.

Roithmayr, Carlos M.↗

NASA NTRS2004

Contributions of Spherical Harmonics to Magnetic and Gravitational Fields

Gravitational forces are of cardinal importance in the dynamics of spacecraft; magnetic attractions sometime play a significant role also, as was the case with the Long Duration Exposure Facility, and as is now true for the first segment of Space Station Freedom. Both satellites depend on gravitational moment and a device known as a magnetic damper to stabilize their orientation. Magnetic fields are mathematically similar to gravitational fields in one important respect: each can be regarded as a gradient of a potential function that, in turn, can be described as an infinite series of spherical harmonics. Consequently, the two fields can be computed, in part, with quantities that need only be evaluated once, resulting in a savings of time when both fields are needed. The objective of this material is to present magnetic field and gravitational force expressions, and point out the terms that belong to both this is accomplished in Section 1 and 2. Section 3 contains the deductive reasoning with which one obtains the expressions of interest. Finally, examples in Section 4 show these equations can be used to reproduce others that arise in connection with special cases such as the magnetic field produced by a tilted dipole, and gravitational force exerted by an oblate spheroid. The mathematics are discussed in the context of terrestrial fields; however, by substituting appropriate constants, the results can be made applicable to fields belonging to other celestial bodies. The expressions presented here share the characteristics of algorithms set forth for computing gravitational force. In particular, computation is performed speedily by means of recursion formulae, and the expressions do not suffer from the shortcoming of a singularity when evaluated at points that lie on the polar axis.

Roithmayr, Carlos M.↗

NASA NTRS2003

Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

Roithmayr, Carlos M.↗

NASA NTRS2003

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

Roithmayr, Carlos M.↗

NASA NTRS2002

Comet/Asteroid Protection System (CAPS): A Space-Based System Concept for Revolutionizing Earth Protection and Utilization of Near-Earth Objects

There exists an infrequent, but significant hazard to life and property due to impacting asteroids and comets. There is currently no specific search for long-period comets, smaller near-Earth asteroids, or smaller short-period comets. These objects represent a threat with potentially little or no warning time using conventional ground-based telescopes. These planetary bodies also represent a significant resource for commercial exploitation, long-term sustained space exploration, and scientific research. The Comet/Asteroid Protection System (CAPS) would expand the current detection effort to include long-period comets, as well as small asteroids and short-period comets capable of regional destruction. A space-based detection system, despite being more costly and complex than Earth-based initiatives, is the most promising way of expanding the range of detectable objects, and surveying the entire celestial sky on a regular basis. CAPS is a future spacebased system concept that provides permanent, continuous asteroid and comet monitoring, and rapid, controlled modification of the orbital trajectories of selected bodies. CAPS would provide an orbit modification system capable of diverting kilometer class objects, and modifying the orbits of smaller asteroids for impact defense and resource utilization. This paper provides a summary of CAPS and discusses several key areas and technologies that are being investigated.

Mazanek, Daniel D.↗

NASA NTRS2001

Integrated Orbit, Attitude, and Structural Control Systems Design for Space Solar Power Satellites

The major objective of this study is to develop an integrated orbit, attitude, and structural control systems architecture for very large Space Solar Power Satellites (SSPS) in geosynchronous orbit. This study focuses on the 1.2-GW Abacus SSPS concept characterized by a 3.2 x 3.2 km solar-array platform, a 500-m diameter microwave beam transmitting antenna, and a 500 x 700 m earth-tracking reflector. For this baseline Abacus SSPS configuration, we derive and analyze a complete set of mathematical models, including external disturbances such as solar radiation pressure, microwave radiation, gravity-gradient torque, and other orbit perturbation effects. The proposed control systems architecture utilizes a minimum of 500 1-N electric thrusters to counter, simultaneously, the cyclic pitch gravity-gradient torque, the secular roll torque caused by an offset of the center-of-mass and center-of-pressure, the cyclic roll/yaw microwave radiation torque, and the solar radiation pressure force whose average value is about 60 N.

Wie, Bong↗

NASA NTRS1999

International Space Station Attitude Control and Energy Storage Experiment: Effects of Flywheel Torque

The Attitude Control and Energy Storage Experiment is currently under development for the International Space Station; two counter-rotating flywheels will be levitated with magnetic bearings and placed in vacuum housings. The primary objective of the experiment is to store and discharge energy, in combination with existing batteries, into the electrical power system. The secondary objective is to use the flywheels to exert torque on the Station; a simple torque profile has been designed so that the Station's Control Moment Gyroscopes will be assisted in maintaining torque equilibrium attitude. Two energy storage contingencies could result in the inadvertent application of torque by the flywheels to the Station: an emergency shutdown of one flywheel rotor while the other remains spinning, and energy storage with only one rotor instead of the counterrotating pair. Analysis of these two contingencies shows that attitude control and the microgravity environment will not be adversely affected.

Roithmayr, Carlos M.↗

NASA NTRS1999

International Space Station Attitude Motion Associated With Flywheel Energy Storage

Flywheels can exert torque that alters the Station's attitude motion, either intentionally or unintentionally. A design is presented for a once planned experiment to contribute torque for Station attitude control, while storing or discharging energy. Two contingencies are studied: the abrupt stop of one rotor while another rotor continues to spin at high speed, and energy storage performed with one rotor instead of a counter rotating pair. Finally, the possible advantages to attitude control offered by a system of ninety-six flywheels are discussed.

Roithmayr, Carlos M.↗

NASA NTRS1993

Computational Control Workstation: Users' perspectives

A Workstation has been designed and constructed for rapidly simulating motions of rigid and elastic multibody systems. We examine the Workstation from the point of view of analysts who use the machine in an industrial setting. Two aspects of the device distinguish it from other simulation programs. First, one uses a series of windows and menus on a computer terminal, together with a keyboard and mouse, to provide a mathematical and geometrical description of the system under consideration. The second hallmark is a facility for animating simulation results. An assessment of the amount of effort required to numerically describe a system to the Workstation is made by comparing the process to that used with other multibody software. The apparatus for displaying results as a motion picture is critiqued as well. In an effort to establish confidence in the algorithms that derive, encode, and solve equations of motion, simulation results from the Workstation are compared to answers obtained with other multibody programs. Our study includes measurements of computational speed.

Roithmayr, Carlos M.↗

NASA NTRS1992

Motion of a spacecraft with magnetic damper

Three methods of numerically simulating the motion of a spacecraft with a magnetic damper are compared. Simulations of motion of the initial assembly stage of Space Station Freedom show that results obtained with the first approach are in general agreement with those based on the second approach, while results from the third method are incorrect unless the spacecraft is nearly at rest in a local-vertical-local-horizontal reference frame. Simulations based on the second method proceed much more quickly than simulations based on the first. An integral of equations of motion governing the behavior of a spacecraft, and a sphere, which is part of the damper is presented. The integral can be used to test the results of numerical integrations performed in connection with the first and second approaches.

Roithmayr, Carlos M.↗

NASA NTRS1991

Contribution of zonal harmonics to gravitational moment

It is presently demonstrated that a recursive vector-dyadic expression for the contribution of a zonal harmonic of degree n to the gravitational moment about a small body's center-of-mass is obtainable with a procedure that involves twice differentiating a celestial body's gravitational potential with respect to a vector. The recursive property proceeds from taking advantage of a recursion relation for Legendre polynomials which appear in the gravitational potential. The contribution of the zonal harmonic of degree 2 is consistent with the gravitational moment exerted by an oblate spheroid.

Roithmayr, Carlos M.↗

NASA NTRS1990

Contribution of zonal harmonics to gravitational moment

A celestial body produces a gravitational moment about the mass center of a small orbiting body, which affects the orientation of the smaller body. Each zonal harmonic in the gravitational potential of a celestial body is shown to make a contribution to the gravitational moment which can be expressed in a recursive vector-dyadic form. A formal derivation is presented, followed by an example in which the result is employed in obtaining the contribution of the zonal harmonic of 2nd degree. The contribution of the zonal harmonic of 3rd degree is also reported.

Roithmayr, Carlos M.↗

NASA NTRS1989

Gravitational moment exerted on a small body by an oblate body

The present demonstration of a method for obtaining vector-dyadic expressions of the gravitational moment about a body's center-of-mass proceeds through the derivation of an expression for the gravitational moment exerted by an oblate spheroid. The contribution of the earth's oblateness to the gravitational moment exerted on a body has been numerically evaluated for a greatly simplified illustrative case; this contribution is noted to be significant by comparison with such other external moments as those exerted by aerodynamic forces.

Roithmayr, Carlos M.↗