Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Jovanović, Božidar"'
Autor:
Jovanovic, Bozidar
We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural objects for
Externí odkaz:
http://arxiv.org/abs/2407.06231
Autor:
Jovanovic, Bozidar
In this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2403.01114
Autor:
Jovanovic, Bozidar
We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between classical mecha
Externí odkaz:
http://arxiv.org/abs/2305.13496
Autor:
Jovanovic, Bozidar, Lukic, Katarina
Publikováno v:
J. Phys. A: Math. Theor. 56 (2023) 015201 (18pp)
Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the non-commutativ
Externí odkaz:
http://arxiv.org/abs/2212.09427
We consider the nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with the same radius $r$ that are rolling without slipping about a fixed sphere $\mathbf S_0$ with center $O$ and radius $R$. In addition, it is assumed tha
Externí odkaz:
http://arxiv.org/abs/2210.11586
Publikováno v:
Regular and Chaotic Dynamics, 2022, Vol. 27, No. 4, pp. 424-442
We first construct nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with centers $O_1,...,O_n$ and with the same radius $r$ that are rolling without slipping around a fixed sphere $\mathbf S_0$ with center $O$ and radius
Externí odkaz:
http://arxiv.org/abs/2208.03009
Publikováno v:
Journal of Nonlinear Science (2023)
We introduce and study the Chaplygin systems with gyroscopic forces. This natural class of nonholonomic systems has not been treated before. We put a special emphasis on the important subclass of such systems with magnetic forces. The existence of an
Externí odkaz:
http://arxiv.org/abs/2110.09938
We present an integrable nonholonomic case of rolling without sliding of a gyroscopic ball over a sphere. This case was introduced and studied in detail by Vasilije Demchenko in his 1923 doctoral dissertation defended at the University of Belgrade, w
Externí odkaz:
http://arxiv.org/abs/2011.03866
Publikováno v:
Regular and Chaotic Dynamics, Vol. 28 (2023) pp. 44-61
In 1983 Bogoyavlenski conjectured that if the Euler equations on a Lie algebra $\mathfrak g_0$ are integrable, then their certain extensions to semisimple lie algebras $\mathfrak g$ related to the filtrations of Lie algebras $\mathfrak g_0\subset \ma
Externí odkaz:
http://arxiv.org/abs/1912.03199
Publikováno v:
Regular and Chaotic Dynamics, 2018, Vol. 23, 289--308
In the review we describe a relation between the Heisenberg spin chain model on pseudospheres and light--like cones in pseudo--Eucli\-dean spaces and virtual billiards. A geometrical interpretation of the integrals associated to a family of confocal
Externí odkaz:
http://arxiv.org/abs/1808.10783