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

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