An Energy Theorem for Developing Testing Functions for Numerical Simulations of Dynamic Systems

1995 ◽  
Vol 117 (2) ◽  
pp. 193-198 ◽  
Author(s):  
C. Q. Liu ◽  
R. L. Huston
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Dynamic Systems ◽  
Mechanical Systems ◽  
Nonholonomic Systems ◽  
Conservation Principle ◽  
Kane’S Equations ◽  
Kane's Equations

This paper presents a kinetic energy theorem, applicable with simple nonholonomic systems. The theorem provides a basis for developing testing functions for measuring the accuracy of numerical simulations—even where no classical conservation principle is applicable. The theorem is established using Kane’s equations for general mechanical systems. A set of general testing functions are then developed. Several examples are presented.

Bond Graphs for Nonholonomic Dynamic Systems

1976 ◽  
Vol 98 (4) ◽  
pp. 361-366 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Dynamic Systems ◽  
Broad Class ◽  
Nonholonomic Systems ◽  
The Other ◽  
Bond Graphs ◽  
Generalized Potential ◽  
Engineering Significance ◽  
Nonholonomic Dynamic Systems

Two very different dynamic systems, one holonomic and the other nonholonomic, can have identical expressions for generalized kinetic energy, generalized potential energy, and transformational constraints between the generalized velocities, and therefore might be confused. Bond graphs for a broad class of nonholonomic systems are shown to differ from their holonomic counterparts simply by the deletion of certain gyrators. Simple examples suggest the engineering significance of nonholonomic systems.

A fresh insight into Kane's equations of motion

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 498-510 ◽  
Author(s):  
H. Nejat Pishkenari ◽  
S. A. Yousefsani ◽  
A. L. Gaskarimahalle ◽  
S. B. G. Oskouei
Keyword(s):  
Dynamic Systems ◽  
Rapid Development ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Impulsive Forces ◽  
Multi Body ◽  
Fresh Insight

SUMMARYWith rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

THE LAGRANGIAN DERIVATION OF KANE’S EQUATIONS

2007 ◽  
Vol 31 (4) ◽  
pp. 407-420 ◽  
Author(s):  
Kourosh Parsa
Keyword(s):  
Kinetic Energy ◽  
Partial Derivative ◽  
Equations Of Motion ◽  
Forward Kinematics ◽  
Body System ◽  
Generalized Coordinates ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Multi Body ◽  
Velocity Level

The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forward kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, the partial derivative of kinetic energy with respect to the system generalized coordinates is specially cumbersome. In this paper, we will derive this partial derivative using a novel kinematic relation for the partial derivative of angular velocity with respect to the system generalized coordinates. It will be shown that, as a result of the use of this relation, the equations of motion of the system are directly derived in the form of Kane’s equations.

Heat Transfer Increase by Flow Structures Modifications

2005 ◽  
Author(s):  
Charles-Andre´ Lemarie´ ◽  
Nachida Bourabaa ◽  
Franc¸ois Monnoyer ◽  
Tewfik Benazzouz
Keyword(s):  
Heat Transfer ◽  
Simple Model ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Experimental Tests ◽  
Flow Structures ◽  
Driven Cavity ◽  
Simple Geometry ◽  
Through Flow ◽  
Do So

This paper makes use of a new methodology for heat transfer increase through flow structures modifications. Intended to help railway designers in handling cooling issues, it is applied to improve the roof-mounted equipment design of a modern railway coach, namely the CORADIA TER 2N NG produced by the ALSTOM Transport company. The brake resistor, a key equipment in charge of dissipating the train kinetic energy as heat into the surrounding air during braking phases, has been particularly considered. To do so, a simple model including a heated obstacle inside a three-sided lead-driven cavity is used, and simple geometry variations are suggested. Their impact on heat transfer is then estimated through numerical simulations while experimental tests validate the results obtained.

On the Comparison of the Dynamic Performance of Open-Loop and Closed-Loop Mechanisms

2014 ◽  
Author(s):  
Jahangir Rastegar ◽  
Dake Feng
Keyword(s):  
Dynamic Response ◽  
Dynamic Systems ◽  
Closed Loop ◽  
Dynamic Performance ◽  
Mechanical Systems ◽  
Open Loop ◽  
Actuation Devices

In general, mechanical systems with closed-loop mechanisms can achieve significantly higher operating speeds as compared to open-loop mechanisms such as robots performing identical tasks. In this brief paper, the reason for the superior dynamic performance of closed-loop mechanisms as compared to open-loop mechanisms performing identical tasks is shown to be the inherent dynamic response limitations of the actuation devices in open-loop dynamic systems. Several examples are provided.

scholarly journals Dynamic and Sensitivity Analysis General Non-Conservative Asymmetric Mechanical Systems

2018 ◽  
Vol 68 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Milan Žmindák
Keyword(s):  
Sensitivity Analysis ◽  
Modal Analysis ◽  
Dynamic Systems ◽  
Mechanical Systems ◽  
Conservative System ◽  
Eigenvalues And Eigenvectors ◽  
Linear Dynamic Systems ◽  
Discretization Methods ◽  
Linear Dynamic ◽  
Derivatives Of

AbstractIn this paper the concept of generalized form of proportional damping is proposed. Classical modal analysis of non-conservative continua is extended to multi DOF linear dynamic systems with asymmetric matrices. Mode orthogonality relationships have been generalized to non-conservative systems. Several discretization methods of continua are presented. Finally, an expression for derivatives of eigenvalues and eigenvectors of non-conservative system is presented. Examples are provided to illustrate the proposed methods.

Sign in / Sign up

Export Citation Format

Share Document