On the dynamics of systems with one-sided non-integrable constraints.

*(English)*Zbl 1474.70018Summary: In the paper we take the first steps in studying the dynamics of systems with one-sided differential constraints defined by inequalities in the phase space. We give a general definition of motion for systems with such constraints. Within the framework of the classical non-holonomic model, and also for systems with servoconstraints (according to Béghin), we present the conditions under which the system leaves two-sided differential constraints. As an example, we consider the Chaplygin sleigh with a one-sided constraint, which is realized by means of an anisotropic force of viscous friction. Variational principles for the determination of motion of systems with one-sided differential constraints are presented.

##### MSC:

70F25 | Nonholonomic systems related to the dynamics of a system of particles |

70H45 | Constrained dynamics, Dirac’s theory of constraints |

##### Keywords:

non-integrable constraints; servoconstraints; non-holonomic mechanics; vakonomic mechanics; one-sided constraint; unilateral constraint
PDF
BibTeX
XML
Cite

\textit{V. V. Kozlov}, Theor. Appl. Mech. (Belgrade) 46, No. 1, 1--14 (2019; Zbl 1474.70018)

Full Text:
DOI

**OpenURL**

##### References:

[1] | V. V. Kozlov,Principles of dynamics with servoconstraints, Vestn. Mosk. Univ., Ser. I5(1989), 59-66. [in Russian] · Zbl 0850.70093 |

[2] | C. G. J. Jacobi,Vorlesungen ¨uber Analytische Mechanik (1847-1848), Vieweg, Braunschweig/Wiesbaden, 1996. |

[3] | V. F. Zhuravlev,Notion of constraint in analytical mechanics, Neline˘ın. Din.8(4) (2012), 853- 860. |

[4] | Yu. I. Neimark, N. A. Fufaev,Dynamics of nonholonomic systems, Transl. Math. Monogr.33, Providence, R.I.: Amer. Math. Soc. 1972. · Zbl 0245.70011 |

[5] | M. V. Deryabin, V. V. Kozlov,On the theory of systems with unilateral constraints, J. Appl. Math. Mech.59(4) (1995), 505-512. · Zbl 0925.70143 |

[6] | V. V. Kozlov,A constructive method for justifying the theory of systems with nonretaining constraints, J. Appl. Math. Mech.52(6) (1988), 691-699. · Zbl 0711.70021 |

[7] | P. Appell,Trait´e de M´ecanique Rationnelle, Gauthier-Villars, Paris, 1904. |

[8] | V. V. Kozlov,Realization of nonintegrable constraints in classical mechanics, Sov. Phys. Dokl. 28(1983), 735-737. · Zbl 0579.70014 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.