TY - JOUR

T1 - Relationship between the Udwadia–Kalaba equations and the generalized Lagrange and Maggi equations

AU - Zegzhda, S. A.

AU - Naumova, N. V.

AU - Soltakhanov, Sh. Kh.

AU - Yushkov, M. P.

N1 - Zegzhda, S.A., Naumova, N.V., Soltakhanov, S.K. et al. Relationship between the Udwadia–Kalaba equations and the generalized Lagrange and Maggi equations. Vestnik St.Petersb. Univ.Math. 49, 81–84 (2016). https://doi.org/10.3103/S1063454116010143

PY - 2016/1

Y1 - 2016/1

N2 - In their paper “A New Perspective on Constrained Motion,” F. E. Udwadia and R. E. Kalaba propose a new form of matrix equations of motion for nonholonomic systems subject to linear nonholonomic second-order constraints. These equations contain all of the generalized coordinates of the mechanical system in question and, at the same time, they do not involve the forces of constraint. The equations under study have been shown to follow naturally from the generalized Lagrange and Maggi equations; they can be also obtained using the contravariant form of the motion equations of a mechanical system subjected to nonholonomic linear constraints of second order. It has been noted that a similar method of eliminating the forces of constraint from differential equations is usually useful for practical purposes in the study of motion of mechanical systems subjected to holonomic or classical nonholonomic constraints of first order. As a result, one obtains motion equations that involve only generalized coordinates of a mechanical system, which corresponds to the equations in the Udwadia–Kalaba form.

AB - In their paper “A New Perspective on Constrained Motion,” F. E. Udwadia and R. E. Kalaba propose a new form of matrix equations of motion for nonholonomic systems subject to linear nonholonomic second-order constraints. These equations contain all of the generalized coordinates of the mechanical system in question and, at the same time, they do not involve the forces of constraint. The equations under study have been shown to follow naturally from the generalized Lagrange and Maggi equations; they can be also obtained using the contravariant form of the motion equations of a mechanical system subjected to nonholonomic linear constraints of second order. It has been noted that a similar method of eliminating the forces of constraint from differential equations is usually useful for practical purposes in the study of motion of mechanical systems subjected to holonomic or classical nonholonomic constraints of first order. As a result, one obtains motion equations that involve only generalized coordinates of a mechanical system, which corresponds to the equations in the Udwadia–Kalaba form.

KW - nonholonomic mechanics

KW - linear nonholonomic second-order constraints

KW - Udwadia–Kalaba equations

KW - generalized second-order Lagrange equations with multipliers

KW - generalized Maggi equations

UR - https://link.springer.com/article/10.3103/S1063454116010143

M3 - Article

VL - 49

SP - 81

EP - 84

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -