An inversion of Rout's theorem

Ranislav Bulatović

Theoretical and applied mechanics, Tome 17 (1991) no. 1, p. 31 .

Résumé

Let $R_0=R_{02}+R_{0j}+\dots$, $R_{02}\leq0$, $j>2$ and $G=G_j+\dots$, be McLaurin series of reduced force function and matrices of gyroscopic forces for the system reduced from holonomic conservative system with cyclic coordinates. By Direct Liapunov method nonstability of tlie stationary motion is proved for the case $s>[(r-2)/2]$ when the first nontrivial form $\hat R_{0r}$ can be positive ($\hat R_0$ is a restriction of $R_0$ function to the hyperspace $R_{02}=0$).