scholarly journals Fundamental Principles of Lagrangian Dynamics: Mechanical Systems with Non-ideal, Holonomic, and Nonholonomic Constraints

2000 ◽  
Vol 251 (1) ◽  
pp. 341-355 ◽  
Author(s):  
Firdaus E. Udwadia
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Lagrangian Dynamics ◽  
Holonomic And Nonholonomic Constraints

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.

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.

Simulation of Constrained Mechanical Systems — Part I: An Equation of Motion

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
David J. Braun ◽  
Michael Goldfarb
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Equation Of Motion ◽  
Practical Implementation ◽  
Constrained Mechanical Systems ◽  
Energy Correction ◽  
Holonomic And Nonholonomic Constraints ◽  
Error Accumulation ◽  
Simulated Motion ◽  
Correction Terms

This paper presents an equation of motion for numerical simulation of constrained mechanical systems with holonomic and nonholonomic constraints. In order to avoid the error accumulation typically experienced in such simulations, the standard equation of motion is enhanced with embedded force and impulse terms which perform continuous constraint and energy correction along the numerical solution. To avoid interference between the kinematic constraint correction and the energy correction terms, both are derived by taking the geometry of the constrained dynamics rigorously into account. In this light, enforcement of the (ideal) holonomic and nonholonomic kinematic constraints are performed using ideal forces and impulses, while the energy conservation law is considered as a nonideal nonlinear nonholonomic constraint on the simulated motion, and as such it is enforced with nonideal forces. As derived, the equation can be directly discretized and integrated with an explicit ODE solver avoiding the need for expensive implicit integration and iterative constraint stabilization. Application of the proposed equation is demonstrated on a representative example. A more elaborate discussion of practical implementation is presented in Part II of this work.

Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems—Extensions for Higher-Order Continuum Models

1998 ◽  
Vol 120 (1) ◽  
pp. 142-144 ◽  
Author(s):  
Alan A. Barhorst
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Higher Order ◽  
Constrained Motion ◽  
Momentum Exchange ◽  
Contact Impact ◽  
Systematic Formulation ◽  
Impact Motion ◽  
Boundary Equations ◽  
Hybrid Differential Equations

In recent work the author presented a systematic formulation of hybrid parameter multiple body mechanical systems (HPMBS) undergoing contact/impact motion. The method rigorously models all motion regimes of hybrid multiple body systems (i.e., free motion, contact/impact motion, and constrained motion), utilizing minimal sets of hybrid differential equations; Lagrange multipliers are not required. The contact/impact regime was modeled via the idea of instantaneously applied nonholonomic constraints. The technique previously presented did not include the possibility of continuum assumptions along the lines of Timoshenko beams, higher order plate theories, or rational theories considering intrinsic spin-inertia. In this technical brief, the above-mentioned method is extended to include the higher-order continuum assumptions which eliminates the continuum shortfalls from the previous work. The main contributions of this work include: 1) the previous work is rigorously extended, and 2) the fact that coefficients of restitution are not required for modeling the momentum exchange between motion regimes of HPMBS. The field and boundary equations provide the needed extra equations that are used to supply post-collision pointwise relationships for the generalized velocities and velocity fields.

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.

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