On quasi-linear oscillation of the mechanical system

Veljko A. Vujičić

Theoretical and applied mechanics, Tome 4 (1978) no. 1, p. 165 .

Résumé

The question of quasi-linear oscillation with small parameters has been the subject of many papers and monographies. But as still does not exist an acceptable analytical working method for solution of quasi-linear oscillation system with more degrees of freedom, therefore, in this paper is given a generalization of procedure of small parameters [1] for the system of one degree of free oscillation to the mechanical system of more degrees of free oscillation. It is considered ihe system of $N$ points under action of conservative, constraint and nonconservative forces dependent on small parametar, whose différé ntial equation of motion in $2n$-dimensional phase space have the form (1), where the functions $f_\alpha(t)$ are periodical and $\boldsymbol B_\alpha$ continuous on $t$, analytically dependent on canonical variables $q^\alpha$ and $p^\alpha$ and of small by module parameter $\varepsilon$. By developing these functions $\boldsymbol R\alpha$ in power series by $q^\alpha-q_0^\alpha$, $p_\alpha-p_{0\alpha}$ and by supposing the solutions in the form (4), the solutions are found in the form (12) for the nonresonant case of oscillation.