Abstract A self-contained, rigorous treatment of rigid-body dynamics is presented, unifying classical formulations (Newton–Euler, Lagrange, Hamilton) with modern geometric mechanics (Lie groups, momentum maps, reduction, symplectic structure). The monograph develops kinematics, equations of motion, variational principles, constraints, stability and conservation laws, and computational techniques for simulation and control. Emphasis is placed on mathematical rigor: precise definitions, well-posedness results, coordinate-free formulations on SE(3) and SO(3), and proofs of equivalence between formulations.
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This volume focuses on the geometric and physical properties of bodies in motion: Google Books Moment of Inertia (MoI): Abstract A self-contained
Main results (statements; proofs are in corresponding sections) unifying classical formulations (Newton–Euler