Equivalence Transformations of Rational Matrices

1992 ◽  
pp. 40-43
Author(s):  
N.P. Karampetakis ◽  
A.C. Pugh ◽  
A.I.G. Vardulakis
Keyword(s):  
Equivalence Transformations

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

scholarly journals Equivalence transformations in the study of integrability

2014 ◽  
Vol 89 (3) ◽  
pp. 038003 ◽  
Author(s):  
Olena O Vaneeva ◽  
Roman O Popovych ◽  
Christodoulos Sophocleous
Keyword(s):  
Equivalence Transformations

Fundamental Solution via Invariant Approach for a Brain Tumor Model and its Extensions

2014 ◽  
Vol 69 (12) ◽  
pp. 725-732 ◽  
Author(s):  
Andrew G. Johnpillai ◽  
Fazal M. Mahomed ◽  
Saeid Abbasbandy
Keyword(s):  
Brain Tumor ◽  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tumor Models ◽  
Partial Differential ◽  
Equivalence Transformations ◽  
Extended Class

AbstractWe firstly show how one can use the invariant criteria for a scalar linear (1+1) parabolic partial differential equations to perform reduction under equivalence transformations to the first Lie canonical form for a class of brain tumor models. Fundamental solution for the underlying class of models via these transformations is thereby found by making use of the well-known fundamental solution of the classical heat equation. The closed-form solution of the Cauchy initial value problem of the model equations is then obtained as well. We also demonstrate the utility of the invariant method for the extended form of the class of brain tumor models and find in a simple and elegant way the possible forms of the arbitrary functions appearing in the extended class of partial differential equations. We also derive the equivalence transformations which completely classify the underlying extended class of partial differential equations into the Lie canonical forms. Examples are provided as illustration of the results.

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