Kane's equations for a variable mass flexible body system

1998 ◽  
Author(s):  
Arun Banerjee
Keyword(s):  
Variable Mass ◽  
Flexible Body ◽  
Body System ◽  
Kane’S Equations ◽  
Kane's Equations

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.

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.

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.

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