The geometry of Newton’s law and rigid systems. (English) Zbl 1164.70014

The geometry of Newton’s law for a classical free particle in terms of Riemannian geometry is formulated. With respect to the environmental space the intrinsic and extrinsic viewpoints are considered. Multi-particle systems are modeled on the \(n\)-th product of the pattern model. The scheme is applied to discrete rigid systems. The tangent and cotangent environmental space is splitted into three components – the center of mass, the relative velocities and the orthogonal subspace. This splitting yields the classical components of linear and angular momentum (which arise from a purely geometric construction) and a third non standard component. The third projection yields a new explicit formula for the reaction force in the nodes of the rigid constraint.


70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70B10 Kinematics of a rigid body
70Exx Dynamics of a rigid body and of multibody systems
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