4 problems

A mechanical system is described by constraints that may be nonlinear in the velocity. Existence conjecture. The existence of mechanical systems with nonlinear constraints in the v…

Let $\mathbf{v}$ be the vector field given by formula. Consider the equations and the system, together with the linear constraints … for $k=1,\ldots,M$. Existence conjecture. There…

Let $\textsc{Q}$ be the configuration space, let $\lambda_k$ be the functions defining the system, and let … for $j=M+1,\ldots,N$. A vector field is called Cartesian if it generate…

Parity conjecture. Singular points $s_1$ and $s_2$ are non-logarithmic for any odd integer $p$ and logarithmic for any even $p\in\mathbb{Z}^{\ast}$.