Mei symmetry and Mei conserved quantity of nonholonomic systems of non-Chetaev’s type in event space

Abstract

This paper studies the Mei symmetry and Mei conserved quantity of non-Chetaev's type in the event space. The differential equations of motion of non-holonomic s ystems of non-Chetaev's type in event spaces are established. The definition and the criteria of Mei symmetry are given. The condition and the form of Mei conse rved quantity are deduced directly from the Mei symmetry. An example is given to illustrate the application of the results.

Mei Symmetry and Mei Conserved Quantity for a Non-holonomic System of Non-Chetaev's Type with Unilateral Constraints in Nielsen Style

“…Using Eq. ( 35), we can easily verify the criterion equation (20), the constraint equation ( 21) are tenable. Substituting Eqs.…”

“…From Eqs. ( 4), ( 6), ( 7), ( 16), (20), and (22), it follows that if the constraints always exist on the system, the unilateral constraints turn into the bilateral constraint, the system turns into the non-holonomic bilateral constraint system. If the constraints vanish from the system, the system turns into the non-conservative system.…”

“…Criterion 3 For the Nielsen equation ( 7), if the infinitesimal generators ξ 0 , ξ s under the infinitesimal transformations (11) satisfy Eqs. ( 18), (20), and ( 21), then the relative symmetry is called the strictly Mei symmetry of the system.…”

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

“…Zhang [22][23][24][25][26] studied the perturbations of Lie symmetries and adiabatic invariance for holonomic systems, the various symmetries and the conserved quantities for holonomic systems and Birkhoffian systems in event space. Jia et al [27][28][29][30][31] and Hou et al [32][33][34] studied the various symmetries and the conserved quantities of nonholonomic systems of non-Chetaev's type with different conditions in event space. Zhang et al [35] studied the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in event space.…”

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

“…Zhang [27] gave the Hojman conserved quantities of Birkhoffian systems in event space. Jia et al [28] studied the Mei symmetry and Mei conserved quantity of nonholonomic systems of non-Chetaev's type in event space. In 1997, Galiullin et al [29] studied a conformal invariance of a Birkhoffian system.…”