8 problems

Let $(P^{2n+r},\{\,,\,\},H)$ be a manifold equipped with an almost-Poisson structure: a contravariant tensor of rank $2n$ that need not satisfy the Jacobi identity. The tensor is H…

The Chaplygin marble is a nonholonomic system whose vertical rotations are allowed; at the compressed level it is not Hamiltonizable on $T^*SO(3)$. The reduced space is $T^*S^2$. N…

c6-simplicity conjecture. Other multi-dimensional Hamiltonisable Chaplygin nonholonomic systems considered by Jovanovi7c should also be c6-simple.

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 the $k$-bar be the mechanical system of $k$ rigid bars moving in $\mathbb{R}^{n+1}$ subject to a nonholonomic constraint, whose regular configuration points are related to the…

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 $p\in\mathbb{Z}^{\ast}$.