Generalized Langevin theory for many‐body problems in chemical dynamics: The method of partial clamping and formulation of the solute equations of motion in generalized coordinates

1984 ◽  
Vol 81 (6) ◽  
pp. 2776-2788 ◽  
Author(s):  
Steven A. Adelman
Keyword(s):  
Equations Of Motion ◽  
Chemical Dynamics ◽  
Many Body ◽  
Generalized Coordinates

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Dynamics Modeling of Elastic Multibody Systems Using Kane’s Method As Applied to a Flexible Robot

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Component Mode Synthesis ◽  
Flexible Robot ◽  
Dynamics Modeling ◽  
Generalized Coordinates ◽  
Kane’S Method ◽  
Kane's Method ◽  
Elastic Multibody Systems ◽  
Elastic Form

Abstract Generalization of Kane’s equations of motion for elastic multibody systems is considered. Initially, finite element techniques are used to generate the elastic form of generalized coordinates. Then, the number of elastic coordinates are reduced by the component mode synthesis. Finally, Kane’s method is applied to obtain the equations of motion of such systems. Using this method, dynamic model of an elastic robot with one degree of freedom is presented.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

scholarly journals Dynamical Evolution of Stellar Clusters and Associations in the Field of Tidal Forces of the Galaxy

1993 ◽  
Vol 132 ◽  
pp. 183-192 ◽  
Author(s):  
T.S. Kozhanov
Keyword(s):  
Jacobi Equation ◽  
Equations Of Motion ◽  
Dynamical Evolution ◽  
Stellar Clusters ◽  
Many Body ◽  
Tidal Forces ◽  
Elliptic Orbits ◽  
The Galaxy ◽  
The Moment ◽  
The Many

AbstractThe equations of motion of the star-members of the cluster averaged on the elliptic orbits are obtained. These equations take into account the tidal forces of the Galaxy. The generalization of the Lagrange-Jacobi equation and Sundman inequality for non-classical scheme of the many-body problems is revised. The dynamical evolution of the moment of inertia is studied. Some theorems which determine the type of the star motion in the cluster are formulated.

Dynamic Analysis of a Spherical Four Bar Mechanism

1992 ◽  
Author(s):  
J. R. Dooley ◽  
J. M. McCarthy
Keyword(s):  
Equations Of Motion ◽  
Joint Angles ◽  
Euler Parameters ◽  
Generalized Coordinates ◽  
Constraint Equations ◽  
Spherical Mechanisms ◽  
Input And Output ◽  
Closed Chain ◽  
Concentric Spheres ◽  
Spherical Mechanism

Abstract Spherical mechanisms are designed so that the points in each link are constrained to move on concentric spheres This paper develops the equations of motion for spherical four bar mechanisms. While the kinematics of these linkages have been extensively studied, the dynamics equations do not seem to have been previously derived. As design techniques for these mechanisms become more efficient, the equations of motion are required to evaluate their performance. The complete dynamics equations of a four-bar spherical mechanism are derived using the input and output joint angles and the Euler parameters of the coupler as generalized coordinates. These coordinates provide a convenient representation of the constraint equations associated with the closed chain. An example analysis is provided.

Dynamics of Open and Closed Chain Spherical Mechanisms Using Quaternion Coordinates

1992 ◽  
Author(s):  
J. R. Dooley ◽  
J. M. McCarthy
Keyword(s):  
Quadratic Form ◽  
Equations Of Motion ◽  
General Technique ◽  
Quadratic Constraint ◽  
Generalized Coordinates ◽  
Constraint Equations ◽  
Spherical Mechanisms ◽  
Closed Chain ◽  
Spherical Mechanism ◽  
Moving Bodies

Abstract This paper presents a general technique for deriving the equations of motion for any open or closed chain spherical mechanism. The technique uses quaternion coordinates to represent the position of each rigid body in the mechanism. Thus, if there are n moving bodies in the chain, there are 4n generalized coordinates in the equations of motion. The use of quaternion coordinates results in standardized quadratic constraint relations representing the hinged connections between bodies in the mechanism. These constraint equations augment the equations of motion. This technique has two important features. First, it is specifically adapted to spherical mechanisms and presents all positions as rotations. Second, the quadratic form of the constraint equations simplifies the computation of velocities and accelerations compatible with the constraints. As an example the equations of motion for a closed six bar spherical chain are derived.

On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems

1993 ◽  
Author(s):  
Timothy A. Loduha ◽  
Bahram Ravani
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Relaxation Method ◽  
Nonholonomic Systems ◽  
Dynamical Equations ◽  
Generalized Coordinates ◽  
First Order ◽  
Constraint Relaxation ◽  
Constrained Dynamical Systems ◽  
Generalized Coordinate

Abstract In this paper we present a method for obtaining first-order decoupled equations of motion for multi-rigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or more complex dynamical systems, where the appropriate congruency transformation may be difficult to obtain, we present a constraint relaxation method based on the use of orthogonal complements. The results are illustrated using several examples. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.

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