Symbolic generation of equations of motion for dynamics/control simulation of large flexible multibody space systems.

摘要

The formulation of equations of motion has become crucial in the successful design of very large and flexible space vehicles. This dissertation presents the derivation of explicit equations of motion for multibody flexible space systems via symbolic manipulation. This methodology generates very efficient computational algorithms in a reasonable amount of time and cost. Kane's dynamical equations are used to formulate the equations of motion. The procedure is considered optimal in the sense that it leaves with the analysts the tasks they are trained to perform, while transferring to the computer the manually prohibitive and distasteful algebraic manipulation and long derivation operations. The derivation allows the analysts to freely choose quantities such as the generalized speeds, the angular velocities, and the velocities, thus leading to a very flexible formulation.;The multibody system is idealized as a collection of interconnected bodies arranged in a topological tree configuration with the option that the bodies can form closed loops. The individual bodies in the system are either rigid or flexible. The flexible characteristics of the bodies are described by means of assumed admissible spatial functions. Bodies of the system are interconnected by hinges possessing zero to six degrees of relative motion freedom with unrestricted large rigid body motion. Linear or nonlinear springs and/or dampers can be incorporated for each degree of freedom at the hinge. Constraints in the multibody system are either holonomic or nonholonomic. Control systems and the external forces and torques acting on the multibody system are easily incorporated into the mathematical model. The explicit nonlinear differential equations of motion are casted in the form ;A general purpose program, named SYMBOD, written in a symbolic manipulation language is developed to generate the explicit equations of motion and is applied to two example problems.