Engineering topics
Publications and source records attributed to Chan, F. K..
The method circumvents many of the existing difficulties in computational logic presently encountered in the direct analytical or numerical evaluation of the appropriate surface integral. It may be applied to complex spacecraft structures for computing the total force arising from either specular or diffuse reflection or even from non-Lambertian reflection and re-radiation.
The analysis covers topics such as time average population, average population times and also the percentage visibility times for a given number of satellites. These results are useful for specific communications satellite applications. Numerical results are obtained for various configurations of a ground station and a ship.
The formulation is rigorous and includes all misalignment angles of the VISSR, the sun sensor and the instantaneous spin axis with the satellite's body axis. It also includes the effects due to the motion of the satellite's suborbital point. All the mapping equations for distortion removal were reduced to simplest forms, and all the algorithms were optimized as much as possible. An approach was then formulated for implementing these algorithms for in-line operational use. It is concluded that in-line distortion removal is possible in real-time processing of infra-red but not visible VISSR imagery data.
An investigation was performed to determine the feasibility of using a two plate model to approximate the Tracking and Data Relay Satellite (TDRS) in orbit propagation, taking into account the effects of solar radiation pressure. The two plate model comprises one plate which always points to the Earth, and the other which is hinged to an axis normal to the orbital plane and is always rotated so that its normal makes a minimum angle with the direction of the sun. The results indicate that it is sufficient to take three parameters, the areas of the two plates and the reflectivity of the Earth pointing plate, to achieve an accuracy of one meter during a 24 hour orbit propagation.
A quadrilateralized spherical cube was constructed to form the basis for the rapid storage and retrieval of high resolution data obtained of the Earth's surface. The structure of this data base was derived from a spherical cube, which was obtained by radially projecting a cube onto its circumscribing sphere. An appropriate set of curvilinear coordinates were chosen such that the resolution cells on the spherical cube were of equal area and were also of essentially the same shape. The main properties of the Earth data base were that the indexing scheme was binary and telescopic in nature, the resolution cells were strung together in a two dimensional manner, the cell addresses were easily computed, and the conversion from geographic to data base coordinates was comparatively simple. It was concluded that this data base structure was perhaps the most viable one for handling remotely sensed data obtained by satellites.
For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.
A study is made of the mathematical solution of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field, using S (Schwarzschild-like) coordinates. A qualitative solution of this equation leads to the conclusion that there can only be 25 different types of orbits. For each value of a, the results are presented in a master diagram for which h and e are the parameters. A master diagram divides the h, e parameter space into regions such that at each point within one of these regions the types of admissible orbits are qualitatively the same. A pictorial representation of the physical orbits in the r, phi plane is also given.