Rather than the traditional vector differential equation, this paper introduces rigid body dynamics in a new form, as a matrix differential equation. For a system of nb rigid bodies, the forces are characterized in terms of network theory, and the kinematics are characterized in terms of a directed graph of the connections of all members. The dynamics are characterized by a second order differential equation in a 3 × 2nb configuration matrix. The first contribution of the paper is the dynamic model of a broad class of systems of rigid bodies, characterized in a compact form, requiring no inversion of a variable mass matrix. The second contribution is the derivation of all equilibria as linear in the control variable. The third contribution is the derivation of a linear model of the system of rigid bodies. One significance of these equations is the exact characterization of the statics and dynamics of all class 1 tensegrity structures, where rigid bar lengths are constant and the string force densities are control variables. The form of the equations allow much easier integration of structure and control design since the control variables appear linearly. This is a significant help to the control design tasks.
- rigid body dynamics