Publications

A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.

A method is presented for input torque shaping for three-dimensional slew maneuvers of a precision pointing flexible spacecraft. The method determines the torque profiles for fixed-time, rest-to-rest maneuvers which minimizes a specified performance index. Spacecraft dynamics are formulated in such a manner that the rigid body and flexible motions are decoupled. Furthermore, assembly by making use of finite element analysis results. Input torque profiles are determined by solving an associated optimization problem using dynamic programming. Three example problems are provided to demonstrate the application of the method.

The method of dynamic programming is applied to three example problems dealing with robot trajectory planning. The first two examples involve end-effector tracking of a straight line with rest-to-rest motions of planar two-link and three-link rigid robots. These examples illustrate the usefulness of the method for producing smooth trajectories either in the presence or absence of joint redundancies. The last example demonstrates the use of the method for rest-to-rest maneuvers of a single-link manipulator with a flexible payload. Simulation results for this example display interesting symmetries that are characteristic of such maneuvers. Details concerning the implementation and computational aspects of the method are discussed.

A method is presented for determining the nonlinear stability of undamped flexible structures spinning about a principal axis of inertia. Equations of motion are developed for structures that are free of applied forces and moments. The development makes use of a floating reference frame which follows the overall rigid body motion. Within this frame, elastic deformations are assumed to be given functions of n generalized coordinates. A transformation of variables is devised which shows the equivalence of the equations of motion to a Hamiltonian system with n + 1 degrees of freedom. Using this equivalence, stability criteria are developed based upon the normal form of the Hamiltonian. It is shown that a motion which is spin stable in the linear approximation may be unstable when nonlinear terms are included. A stability analysis of a simple flexible structure is provided to demonstrate the application of the stability criteria. Results from numerical integration of the equations of motion are shown to be consistent with the predictions of the stability analysis. A new method for modeling the dynamics of rotating flexible structures is developed and investigated. The method is similar to conventional assumed displacement (modal) approaches with the addition that quadratic terms are retained in the kinematics of deformation. Retention of these terms is shown to account for the geometric stiffening effects which occur in rotating structures. Computational techniques are developed for the practical implementation of the method. The techniques make use of finite element analysis results, and thus are applicable to a wide variety of structures. Motion studies of specific problems are provided to demonstrate the validity of the method. Excellent agreement is found both with simulations presented in the literature for different approaches and with results from a commercial finite element analysis code. The computational advantages of the method are demonstrated.

A method is presented for smoothing and differentiating noisy data given on a rectangular grid. The method makes use of a one-dimensional smoothing algorithm to construct the solution to an associated two-dimensional problem. Smoothing parameter selection is automated using a technique that does not require prior knowledge of the amount of noise in the data. Numerical examples are provided demonstrating the application of the method. 4 refs., 8 figs., 2 tabs.