Point-connected rigid bodies in a topological tree     

Peter W. Likins 《Celestial Mechanics and Dynamical Astronomy》1975,11(3):301-317

Identical equations of motion are shown to emerge for a system ofn+1 rigid bodies all interconnected byn points, each of which is common to two bodies, by means of each of the following derivation procedures, all of which employ a kinematical identity developed by Hooker and Margulies: The Hooker-Margulies/Hooker equations; Kane's quasicoordinate formulation of D'Alembert's principle; the combination of Lagrange's generalized coordinate equations and Lagrange's quasicoordinate equations; and the combination of Lagrange's generalized coordinate equations and the vector rotational equationM=H applied to the total system and resolved into a vector basis fixed in a reference body of the system. Thus the previously published Hooker-Margulies/Hooker equations are shown to be the natural result of several derivation procedures other than the Newton-Euler method originally used, provided that the central kinematical identity of the original derivation of Hooker and Margulies is employed.  相似文献   

Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft     

Yoshiaki Ohkami  Peter Likins 《Celestial Mechanics and Dynamical Astronomy》1979,19(4):359-390

Literal characterizations are developed for the eigenvalues and eigenvectors of a system of linear time-invariant equations which describes the attitude motion of flexible spacecraft in terms of hybrid coordinates. The eigenproblem is shown to reduce to that of a symmetric and positive definite matrix of lower dimension. For the zero damping case, both analytical and minimax characterization methods prove to be useful in localizing the eigenvalues, and eigenvectors for systems of large dimension are obtained explicitly in terms of a 3×1 matrix whose elements are available from a system of three algebraic equations provided.  相似文献   

Matrix method for the Liapunov stability analysis of cyclic discrete mechanical systems     

Peter W. Likins  Robert E. Roberson 《Celestial Mechanics and Dynamical Astronomy》1971,3(4):491-507

A matrix formalism is developed for the purpose of facilitating the Liapunov stability analysis of discrete, holonomic, mechanical systems with cyclic coordinates and with the Hamiltonian free of explicit time dependence. Matrix expressions are developmed for the kinetic energy, the Routhian, the Hamiltonian, and the quadratic approximation of the dynamic potential energy, with cyclic coordinates, cyclic-coordinate velocities, and cyclic-coordinate generalized momenta not explicitly involved in the last of these functions. The final result is an expression for the quadratic approximation of the dynamic potential energy that is calculated much more readily than by scalar analysis. From the condition for positive-definiteness of this function, Liapunov stability conditions are available. The method is applied to a dual-spin satellite to illustrate the procedure.  相似文献