Servosystems and program motions of mechanical system (Q2782137)

The author studies a mechanical system whose motion is subjected to the conditions of the type NEWLINE\[NEWLINE A_{\mu i}(t,q, \dot q,\dots,\overset{(k-1)} q)\overset{(k)} {q_i} + A_{\mu}(t,q, \dot q,\dots,\overset{(k-1)} q)=0,\quad \text{rang}\,(A_{\mu i}) = l.\tag{1} NEWLINE\]NEWLINE Under restriction (1), the author obtains \(n\) differential equations of the order of \(\,s\geq k\,\) with \(l\) Lagrangian multiplies which become the Beghen's equations (see [\textit{A.~Beghen}, ``Theory of gyroscopic compasses'', Nauka, Moscow (1967)]), for \(\,s=2\,\) and \(\,k=1\). Besides, the additional initial conditions are assumed to be arbitrary.