scholarly journals A new form of equations of motion of nonholonomic mechanical systems

1997 ◽  
Vol 19 (3) ◽  
pp. 59-64
Author(s):  
Do Sanh
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Matrix Form ◽  
Inverse Matrix ◽  
Nonholonomic Mechanical Systems ◽  
Solution Of Equations ◽  
The Matrix ◽  
New Form

In the paper it is given a new form of equations of motion of nonholonomic mechanical systems. The obtained equations are written in a matrix form and in order to establish them it is unnecessary to calculate the inverse matrix of the matrix of inertia. It is important that it is possible to obtain the relation between the error of realizing constraints and that of computing the solution of equations of motion of the system under consideration.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

A geometric approach to the transpositional relations in dynamics of nonholonomic mechanical systems

2018 ◽  
Vol 15 (07) ◽  
pp. 1850112 ◽  
Author(s):  
Mahdi Khajeh Salehani
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Geometric Approach ◽  
Nonholonomic Mechanical Systems ◽  
Nonholonomic Dynamics ◽  
Geometric Objects

Exploring the geometry of mechanical systems subject to nonholonomic constraints and using various bundle and variational structures intrinsically present in the nonholonomic setting, we study the structure of the equations of motion in a way that aids the analysis and helps to isolate the important geometric objects that govern the motion of such systems. Furthermore, we show that considering different sets of transpositional relations corresponding to different transitivity choices provides different variational structures associated with nonholonomic dynamics, but the derived equations (being referred to as the generalized Hamel–Voronets equations) are equivalent to the Lagrange–d’Alembert equations. To illustrate results of this work and as some applications of the generalized Hamel–Voronets formalisms discussed in this paper, we conclude with considering the balanced Tennessee racer, as well as its modification being referred to as the generalized nonholonomic cart, and an [Formula: see text]-snake with three wheeled planar platforms whose snake-like motion is induced by shape variations of the system.

Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement

1991 ◽  
Vol 58 (1) ◽  
pp. 238-243 ◽  
Author(s):  
Subir Kumar Saha ◽  
Jorge Angeles
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Rigid Bodies ◽  
Orthogonal Complement ◽  
Constraint Equations ◽  
Nonholonomic Mechanical Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Automatic Guided Vehicle ◽  
The Matrix ◽  
Velocity Constraint

The dynamics equations governing the motion of mechanical systems composed of rigid bodies coupled by holonomic and nonholonomic constraints are derived. The underlying method is based on a natural orthogonal complement of the matrix associated with the velocity constraint equations written in linear homogeneous form. The method is applied to the classical example of a rolling disk and an application to a 2-dof Automatic Guided Vehicle is outlined.

On the Lagrangian Formalism of Nonholonomic Mechanical Systems

2005 ◽  
Author(s):  
Hiroaki Yoshimura
Keyword(s):  
Mechanical System ◽  
Tangent Bundle ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Lagrangian System ◽  
Lagrangian Formalism ◽  
Nonholonomic Mechanical Systems ◽  
Points Of View ◽  
Configuration Manifold

The paper illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d’Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d’Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

scholarly journals Differential equations of motion in matrix form of a multibody system driven by electric motors

2019 ◽  
Author(s):  
Nguyen Quang Hoang ◽  
Vu Duc Vuong
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Matrix Form ◽  
Electric Motors ◽  
Electromechanical Systems ◽  
Current Variation

This paper presents the dynamic model of multibody systems driven by electric motors, the so-called electromechanical systems. The mechanical systems considered in this study include an open loop and/or a closed loop, a full-actuated and an under-actuated one. The dynamic model of this electromechanical systems is established in matrix form by applying the Lagrangian equation with and without multipliers and substructure method. With this approach it is easy to obtain the differential equation of motion of the electro-mechanical systems based on the corresponding differential equations of the purely available mechanical system. These obtained equations describe the electromechanical systems in engineering better than in case the systems are purely described by mechanical equations. The differential equations of serial and parallel manipulators, slider-crank mechanism, and overhead crane driven by electric motors are established as illustrated examples. In addition, a simplified dynamic model obtained by neglecting of current variation is also validated by numerical simulation. 

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

Concise Equations for Rotor Dynamics Analysis

1995 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
The Other ◽  
Dynamics Analysis ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Abstract Concise equations for rotor dynamics analysis are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two proposed ordering algorithms lead to more compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. This numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency.

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