On the Transformation Properties of the Nonlinear Hamel Equations

1995 ◽  
Vol 62 (4) ◽  
pp. 924-929 ◽  
Author(s):  
J. G. Papastavridis
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Inertia Force ◽  
Discrete Mechanical Systems ◽  
Inertial Terms ◽  
The Individual ◽  
Boltzmann Hamel Equations ◽  
System Inertia

This paper discusses the transformation properties of the famous Johnsen-Hamel equations of motion of discrete mechanical systems in general nonlinear nonholonomic coordinates and constraints (i.e., the nonlinear extension of the well-known Boltzmann-Hamel equations), under general nonlinear (local) quasi-velocity transformations. It is shown that the individual kinematico-inertial terms making up the system inertia force, or system acceleration, such as the nonlinear nonholonomic Euler-Lagrange operator and nonholonomic correction (or deviation) terms, in general, do not transform as nonholonomic covariant vectors; although taken as a whole they do, as expected. This work extends and completes the work of Papastavridis (1994), and it is strongly recommended that it be read after that paper.

On the Boltzmann-Hamel Equations of Motion: A Vectorial Treatment

1994 ◽  
Vol 61 (2) ◽  
pp. 453-459 ◽  
Author(s):  
J. G. Papastavridis
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Discrete Mechanical Systems ◽  
The Common ◽  
Boltzmann Hamel Equations ◽  
Nonlinear Velocity

This paper presents a direct vectorial derivation of the famous Boltzmann-Hamel equations of motion of discrete mechanical systems, in general nonlinear nonholonomic coordinates and under general nonlinear (velocity) nonholonomic constraints. The connection between particle and system vectors is stressed throughout, in all relevant kinematic and kinetic quantities/principles/theorems. The specialization of these results to the common case of linear nonholonomic coordinates and linear nonholonomic (i.e., Pfaffian) constraints is carried out in the paper’s Appendix.

DYNAMICS OF FLEXIBLE MULTIBODY MECHANICAL SYSTEMS

1991 ◽  
Vol 15 (3) ◽  
pp. 235-256 ◽  
Author(s):  
X. Cyril ◽  
J. Angeles ◽  
A. Misra
Keyword(s):  
Equations Of Motion ◽  
Matrix Multiplication ◽  
Mechanical Systems ◽  
Dynamical Behaviour ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Simple Matrix ◽  
Kinematic Velocity ◽  
Velocity Constraints ◽  
The Individual

In this paper the formulation and simulation of the dynamical equations of multibody mechanical systems comprising of both rigid and flexible-links are accomplished in two steps: in the first step, each link is considered as an unconstrained body and hence, its Euler-Lagrange (EL) equations are derived disregarding the kinematic couplings; in the second step, the individual-link equations, along with the associated constraint forces, are assembled to obtain the constrained dynamical equations of the multibody system. These constraint forces are then efficiently eliminated by simple matrix multiplication of the said equations by the transpose of the natural orthogonal complement of kinematic velocity constraints to obtain the independent dynamical equations. The equations of motion are solved for the generalized accelerations using the Cholesky decomposition method and integrated using Gear’s method for stiff differential equations. Finally, the dynamical behaviour of the Shuttle Remote Manipulator when performing a typical manoeuvre is determined using the above approach.

On Energy Rate Theorems for Linear First-Order Nonholonomic Systems

1991 ◽  
Vol 58 (2) ◽  
pp. 536-544 ◽  
Author(s):  
John G. Papastavridis
Keyword(s):  
Recent Work ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Systems ◽  
General Linear ◽  
Energy Rate ◽  
First Order ◽  
Power Equation ◽  
Boltzmann Hamel Equations ◽  
Power Reaction

Starting with the Boltzmann/Hamel equations of motion of mechanical systems subject to general linear and first-order nonholonomic and rheonomic constraints, and in nonholonomic coordinates, this paper derives the general (reactionless) energy rate, or power, equation for such systems, in a straightforward and physically clear fashion. A power (reaction-containing) equation for these systems, but in holonomic coordinates, is also derived for completeness. An example of a sphere rolling on a uniformly spinning plane serves to illustrate these power theorems. The paper extends and corrects the recent work by Kane and Levinson (1988) on the same topic.

Multirate Integration for Multibody Dynamic Analysis With Decomposed Subsystems

1999 ◽  
Author(s):  
Sung-Soo Kim ◽  
Jeffrey S. Freeman
Keyword(s):  
Dynamic Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Inertia Force ◽  
Integration Scheme ◽  
Integration Algorithm ◽  
Multibody Dynamic ◽  
Higher Order Derivative ◽  
Derivative Information

Abstract This paper details a constant stepsize, multirate integration scheme which has been proposed for multibody dynamic analysis. An Adams-Bashforth Moulton integration algorithm has been implemented, using the Nordsieck form to store internal integrator information, for multirate integration. A multibody system has been decomposed into several subsystems, treating inertia coupling effects of subsystem equations of motion as the inertia forces. To each subsystem, different rate Nordsieck form of Adams integrator has been applied to solve subsystem equations of motion. Higher order derivative information from the integrator provides approximation of inertia force computation in the decomposed subsystem equations of motion. To show the effectiveness of the scheme, simulations of a vehicle multibody system that consists of high frequency suspension motion and low frequency chassis motion have been carried out with different tire excitation forces. Efficiency of the proposed scheme has been also investigated.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

scholarly journals О бародиффузии при медленных течениях газовой смеси

2019 ◽  
Vol 89 (5) ◽  
pp. 646
Author(s):  
В.М. Жданов
Keyword(s):  
Equations Of Motion ◽  
Considerable Effect ◽  
Gas Mixture ◽  
Slip Coefficient ◽  
Knudsen Numbers ◽  
Slow Flows ◽  
Diffusion Slip ◽  
The Mean ◽  
The Individual ◽  
Small Knudsen Numbers

AbstractBarodiffusion in slow flows of a gas mixture is studied with an approximation using hydrodynamic equations of motion for the individual mixture components. It is shown that consideration of the viscous momentum transfer and the contribution of Knudsen layers for the mixture flowing in a channel has a considerable effect on the value of the barodiffusion factor. The relations are obtained for the mean diffusion fluxes of components and for the total flux of the mixture in a circular cylindrical capillary; these relations are valid for moderately small Knudsen numbers used for calculation of the diffusion baroeffect and separation effect when the gas mixture flows in a set of capillaries connecting two volumes. The modification of the relations for the barodiffusion factor (and for the diffusion slip coefficient cross-linked with it) allows interpreting the sign alteration of these effects observed experimentally for some gas mixtures at intermediate Knudsen numbers.

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