Matrix equations of motion of nonholonomic systems. (English. Russian original) Zbl 0779.70012

Velichenko, V. V.

Sov. Phys., Dokl. 36, No. 11, 768-771 (1991); translation from Dokl. Akad. Nauk SSSR 321, No. 3, 499-504 (1991).

The system of \(n\) differential equations \(M(q,t)\ddot q=f(q,\dot q,t)\) with imposed nonholonomic constraints of the type \(J(q,\dot q,t)=0\) or \(\dot q=\gamma(q,\nu,t)\) with a vector \(\nu\) of parameters is investigated. The methods proposed for solving the system are distinct from the traditional ones using virtual velocities. As an example, the motion of a homogeneous ball along a horizontal rough plane is presented.

Reviewer: W.Muschik (Berlin)

MSC:

70F25	Nonholonomic systems related to the dynamics of a system of particles
34A34	Nonlinear ordinary differential equations and systems

Keywords:

matrix-geometrical approach; homogeneous ball; horizontal rough plane