Publications

Online First Articles

• 1.

  Kozlov V. V.

  Solvable Algebras and Integrable Systems
  Regular and Chaotic Dynamics, 2024

  Abstract          pdf  (420.94 Kb)

  This paper discusses a range of questions concerning the application of solvable Lie algebras of vector fields to exact integration of systems of ordinary differential equations. The set of $n$ independent vector fields generating a solvable Lie algebra in $n$-dimensional space is locally reduced to some “canonical” form. This reduction is performed constructively (using quadratures), which, in particular, allows a simultaneous integration of $n$ systems of differential equations that are generated by these fields. Generalized completely integrable systems are introduced and their properties are investigated. General ideas are applied to integration of the Hamiltonian systems of differential equations.

  
  

  Keywords:	quadratures, solvable alebra, Frobenius theorem, completely integrable systems, Lie theorem, Hamiltonian systems
  Citation:	Kozlov V. V., Solvable Algebras and Integrable Systems, Regular and Chaotic Dynamics, 2024, https://doi.org/10.1134/S1560354724520022
  DOI:	10.1134/S1560354724520022
  Full text:	pdf  (420.94 Kb)
• 2.

  Bizyaev I. A., Mamaev I. S.

  Nonlinear Dynamics of a Roller Bicycle
  Regular and Chaotic Dynamics, 2024

  Abstract          pdf  (2.93 Mb)

  In this paper we consider the dynamics of a roller bicycle on a horizontal plane. For this bicycle we derive a nonlinear system of equations of motion in a form that allows us to take into account the symmetry of the system in a natural form. We analyze in detail the stability of straight-line motion depending on the parameters of the bicycle. We find numerical evidence that, in addition to stable straight-line motion, the roller bicycle can exhibit other, more complex, trajectories for which the bicycle does not fall.

  
  

  Keywords:	roller bicycle, nonholonomic system, stability, quasi-velocities, Poincaré map
  Citation:	Bizyaev I. A., Mamaev I. S., Nonlinear Dynamics of a Roller Bicycle, Regular and Chaotic Dynamics, 2024, https://doi.org/10.1134/S1560354724530017
  DOI:	10.1134/S1560354724530017
  Full text:	pdf  (2.93 Mb)