title: Application of a special form of differential equations to the study of motion of a loaded Stewart platform
metadata.name: dc.contributor.author
metadata.value: Zegzhda, Sergey A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Petrova, Victoriya I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Yushkov, Mikhail P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T13:09:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T13:09:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zegzhda S.A., Petrova V. I., Yushkov M.P. Application of a special form of differential equations to the study of motion of a loaded Stewart platform. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 128–140.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.113
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17336
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper is concerned with motions of a loaded Stewart platform. The motion equations
  are composed using a special form of differential equations (motion equations are derived
  in redundant coordinates). This form is also used to derive first-order vector Lagrange
  equations involving differentiation with respect to the radius vector of the system center
  of mass, the unit vectors of the principal central inertia axes of a motion body and with
  respect to these derivatives. These vectors define the position of the rigid body in space.
  As abstract holonomic constraint imposed on the vectors describing the motion of the rigid
  body, one considers the invariableness of the lengths of unit vectors and their orthogonality.
  We discuss one engineering effect manifested in the behavior of a Steward platform in an
  equilibrium state (“parasitic oscillations”). This effect is one of the root causes for the
  system to move away from an unstable equilibrium position. A similar instability is also
  present in standard vertical oscillations of a Stewart platform. A simplest mechanism of
  appearance of instability of such vertical motions of a platform is revealed. To guarantee
  a stable motion, it is proposed introduce the classical feedbacks. Numerical solutions of
  the differential equations thus obtained are in complete accord with the numerical results
  obtained in the solution of the motion equations composed using the of center mass motion
  theorems and taking into account results on the variation of the kinetic moment as the
  system moves about the center of mass.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by the Russian Foundation for Basic Research (grant No. 19.01.00208-а).
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. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Stewart platform
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dynamic simulation bench
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: special form of motion equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: feedbacks
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Application of a special form of differential equations to the study of motion of a loaded Stewart platform
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 128-140.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17336/1/128-140.pdf
resources.format: Adobe PDF
resources.size: 389,95 kB