Automatic elimination of the undetermined multipliers in Kane's equations using a Pseudo Uptriangular Decomposition (PUTD) method

1987 ◽  
Vol 27 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Farid M.L. Amirouche ◽  
Tongyi Jia
Keyword(s):  
Kane’S Equations ◽  
Kane's Equations ◽  
Automatic Elimination

Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

1988 ◽  
Vol 55 (4) ◽  
pp. 899-904 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Null Space ◽  
Computationally Efficient ◽  
New Approach ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Linearly Independent ◽  
Kane's Equations ◽  
Constrained Dynamical Systems ◽  
Coordinate Reduction ◽  
Algebraic Constraint

In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

An Applied Form of Kane’s Equations of Motions

2005 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Amir Lotfi Gaskarimahalle ◽  
Seyed Babak Ghaemi Oskouei ◽  
Ali Meghdari
Keyword(s):  
Degrees Of Freedom ◽  
Control Unit ◽  
Generalized Coordinates ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Angular Velocities ◽  
New Form ◽  
Derivatives Of ◽  
Equations Of Motions

In this paper we have presented a new form of Kane’s equations. This new form is expressed in the matrix form with the components of partial derivatives of linear and angular velocities relative to the generalized speeds and generalized coordinates. The number of obtained equations is equal to the number of degrees of freedom represented in a closed form. Also the equations can be rearranged to appear only one of the time derivatives of generalized speeds in each equation. This form is appropriate especially when one intends to derive equations recursively. Hence in addition to the simplicity, the amount of calculations is noticeably reduced and also can be used in a control unit.

Extended Kane’s Equations for Nonholonomic Variable Mass System

1982 ◽  
Vol 49 (2) ◽  
pp. 429-431 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-H. Cheng
Keyword(s):  
Equations Of Motion ◽  
Variable Mass ◽  
Mass System ◽  
Variable Mass System ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Variable Mass Systems

An extension of Kane’s equations of motion for nonholonomic variable mass systems is presented. As an illustrative example, equations of motion are formulated for a rocket car.

Kane’s Equations With Undetermined Multipliers—Application to Constrained Multibody Systems

1987 ◽  
Vol 54 (2) ◽  
pp. 424-429 ◽  
Author(s):  
J. T. Wang ◽  
R. L. Huston
Keyword(s):  
Multibody Systems ◽  
Automated Analysis ◽  
Numerical Analyses ◽  
Constrained Multibody Systems ◽  
Controlled Systems ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

A procedure for automated analysis of constrained multibody systems is presented. The procedure is based upon Kane’s equations and the concept of undetermined multipliers. It is applicable with both free and controlled systems. As with Lagrange’s equations, the multipliers are identified as scalar components of constraining forces and moments. The advantage of using Kane’s equations is that they are ideally suited for development of algorithms for numerical analyses. Also, generalized speeds and quasi-coordinates are readily accommodated. A simple example illustrating the concepts is presented.

Sign in / Sign up

Export Citation Format

Share Document