scholarly journals Hamilton–Jacobi theory for degenerate Lagrangian systems with holonomic and nonholonomic constraints

2012 ◽  
Vol 53 (7) ◽  
pp. 072905 ◽  
Author(s):  
Melvin Leok ◽  
Tomoki Ohsawa ◽  
Diana Sosa
Keyword(s):  
Nonholonomic Constraints ◽  
Lagrangian Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Degenerate Lagrangian

Simulation of Constrained Mechanical Systems—Part II: Explicit Numerical Integration

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
David J. Braun ◽  
Michael Goldfarb
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Direct Consequence ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Constrained Motion ◽  
Constrained Mechanical Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Long Time ◽  
Constraint Correction

This paper presents an explicit to integrate differential algebraic equations (DAEs) method for simulations of constrained mechanical systems modeled with holonomic and nonholonomic constraints. The proposed DAE integrator is based on the equation of constrained motion developed in Part I of this work, which is discretized here using explicit ordinary differential equation schemes and applied to solve two nontrivial examples. The obtained results show that this integrator allows one to precisely solve constrained mechanical systems through long time periods. Unlike many other implicit DAE solvers which utilize iterative constraint correction, the presented DAE integrator is explicit, and it does not use any iteration. As a direct consequence, the present formulation is simple to implement, and is also well suited for real-time applications.

scholarly journals A new method for determining the reactions of mechanical constraints

2006 ◽  
Vol 28 (1) ◽  
pp. 35-42
Author(s):  
Do Sanh ◽  
Do Dang Khoa
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraints ◽  
Inverse Matrix ◽  
Algebraic Equations ◽  
Closed Set ◽  
Mechanical Constraints ◽  
Large Size ◽  
Holonomic And Nonholonomic Constraints ◽  
The Matrix ◽  
Lagrange’S Multipliers

In the present paper it is introduced the method for determining the reactions of mechanical constraints (holonomic and nonholonomic constraints).As is known, for studying dynamical characters of a mechanical system it is necessary to determine the constraint reactions acting on the system. Up to now, the reactions are calculated through Lagrange's multipliers. By such a way the reactions are determined only indirectly. In the [3, 4], two methods of determining directly the reactions are discussed. However, for applying these methods, it is necessary to compute the inverse matrix of the matrix of inertia. This thing in general is not convenient, specially when the matrix of inertial is of large size and dense.In the present paper it is represented the method for determining the constraint reactions, by which it is possible to avoid inertia the computation of the inverse matrix of the matrix of inertia is avoided. For this in the paper it is used the middle variables by which we obtain a closed set of algebraic equations for directly determining reactions.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

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.

Selective Generalized Coordinates Partitioning Method for Multibody Systems With Non-Holonomic Constraints

2017 ◽  
Author(s):  
Ayman A. Nada ◽  
Abdullateef H. Bashiri
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Research Work ◽  
Nonholonomic Constraints ◽  
Integration Step ◽  
Large Scale Systems ◽  
Holonomic Constraints ◽  
Generalized Coordinates ◽  
Holonomic And Nonholonomic Constraints ◽  
Multi Body

The goal of this research work is to extend the method of generalized coordinates partitioning to include both holonomic and nonholonomic constraints. Furthermore, the paper proposes a method for selective coordinates for integration instead of identifying a set of independent coordinates at each integration step. The effectiveness of the proposed method is presented and compared with full-coordinates integration as well as generalized co-ordinates partitioning method. The proposed method can treat large-scale systems as one of the main advantages of multi-body systems.

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