title: Relationship between the Udwadia—Kalaba equations and the generalized Lagrange and Maggi’s equations
metadata.name: dc.contributor.author
metadata.value: Zegzhda, Sergey A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Naumova, Natalya V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Soltakhanov, Shervani Kh.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Yushkov, Mikhail P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-01T15:28:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-01T15:28:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-03
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3844
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In their paper “A new perspective on constrained motion” F. E. Udwadia and R. E. Kalaba offered a new
  form of matrix equations of motion for nonholonomic systems subject to linear nonholonomic second-order
  constraints. The obtained equations contain all the generalized coordinates of the mechanical system in
  question, and at the same time they do not contain the constraint reaction forces. This is an undoubted
  advantage of the equations presented, so the authors assume that “the equations of motion obtained in
  this paper appear to be the simplest and most comprehensive so far discovered”. To write these equations
  the authors apply a rather specific transformation proposed by Moore already in 1920 and developed by
  Penrose in 1955. In Russian literature it is said that in this case a pseudoinverse matrix is used.
  The present paper reveals that the equations obtained by those authors can be naturally derived from
  the generalized Lagrange and Maggi’s equations or when using a contravariant form of the equations of
  motion of a mechanical system subject to linear nonholonomic second-order constraints. It is noted that a
  similar technique for eliminating the reaction forces from differential equations is usually used in practical
  studying of motion of mechanical systems that are subject to holonomic and classical nonholonomic
  first-order constraints. As a result, we obtain the equations of motion containing only the generalized
  coordinates of a mechanical system, what corresponds to the equations of Udwadia—Kalaba form. Refs 7.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: nonholonomic mechanics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear nonholonomic second-order constraints
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the Udwadia—Kalaba equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the generalized Lagrange equations of second kind with multipliers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized Maggi’s equations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Relationship between the Udwadia—Kalaba equations and the generalized Lagrange and Maggi’s equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Zegzhda_Naumova_et_al.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3844/1/Zegzhda_Naumova_et_al.pdf
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