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

Modugno, Marco; Vitolo, Raffaele

Arch. Math., Brno 43, No. 3, 197-229 (2007).

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.

Reviewer: Josef Janyška (Brno)

MSC:

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

Keywords:

classical mechanics; rigid system; Newton’s law; Riemannian geometry