Abstract
A novel method is presented to solve the equations of motion for a large class of constrained and unconstrained dynamical systems. Given an analytic expression for the system mass matrix, quasivelocity equations of motion are derived in a manner that generates equations analogous to the dynamics/kinematics partitioning in Eulerian rigid body dynamics. This separation is accomplished by introducing a new quasivelocity vector η which yields a dynamical system with an identity mass matrix. The problem of inverting a complex mass matrix is replaced by the problem of solving two first-order differential equations for the mass matrix eigenfactors. Dynamic constraint equations are incorporated directly into the new η differential equation, forgoing any need to solve the algebraic constraint equations simultaneously with the differential equations of motion.
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Junkins, J.L., Schaub, H. An Instantaneous Eigenstructure Quasivelocity Formulation for Nonlinear Multibody Dynamics. J of Astronaut Sci 45, 279–295 (1997). https://doi.org/10.1007/BF03546405
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DOI: https://doi.org/10.1007/BF03546405