Indecomposable second-order matrix rings with a finite number of bass representations

1972 ◽  
Vol 12 (5) ◽  
pp. 797-798 ◽  
Author(s):  
Yu. A. Drozd
Keyword(s):  
Finite Number ◽  
Second Order ◽  
Matrix Rings ◽  
Order Matrix

Number of representation moduli in a genus for integer second-order matrix rings

1967 ◽  
Vol 2 (2) ◽  
pp. 564-566
Author(s):  
Yu. A. Drozd ◽  
V. M. Turchin
Keyword(s):  
Second Order ◽  
Matrix Rings ◽  
Order Matrix

scholarly journals A Markovian canonical form of second-order matrix-exponential processes

2008 ◽  
Vol 190 (2) ◽  
pp. 459-477 ◽  
Author(s):  
L. Bodrog ◽  
A. Heindl ◽  
G. Horváth ◽  
M. Telek
Keyword(s):  
Canonical Form ◽  
Second Order ◽  
Matrix Exponential ◽  
Order Matrix

scholarly journals GEOMETRIC VARIATIONS OF THE BOLTZMANN ENTROPY

2008 ◽  
Vol 22 (15) ◽  
pp. 1447-1454
Author(s):  
NIKOS KALOGEROPOULOS
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Second Order ◽  
Second Variation ◽  
Boltzmann Entropy ◽  
Constant Energy ◽  
The Stability ◽  
The Second Variation

We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.

scholarly journals Feedback Linearisation for Nonlinear Vibration Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. Jiffri ◽  
P. Paoletti ◽  
J. E. Cooper ◽  
J. E. Mottershead
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Problems ◽  
Second Order ◽  
Degree Of Freedom ◽  
Sensors And Actuators ◽  
Order Matrix ◽  
Problem Class ◽  
Aeroelastic Model ◽  
Matrix Differential ◽  
Three Degree Of Freedom

Feedback linearisation is a well-known technique in the controls community but has not been widely taken up in the vibrations community. It has the advantage of linearising nonlinear system models, thereby enabling the avoidance of the complicated mathematics associated with nonlinear problems. A particular and common class of problems is considered, where the nonlinearity is present in a system parameter and a formulation in terms of the usual second-order matrix differential equation is presented. The classical texts all cast the feedback linearisation problem in first-order form, requiring repeated differentiation of the output, usually presented in the Lie algebra notation. This becomes unnecessary when using second-order matrix equations of the problem class considered herein. Analysis is presented for the general multidegree of freedom system for those cases when a full set of sensors and actuators is available at every degree of freedom and when the number of sensors and actuators is fewer than the number of degrees of freedom. Adaptive feedback linearisation is used to address the problem of nonlinearity that is not known precisely. The theory is illustrated by means of a three-degree-of-freedom nonlinear aeroelastic model, with results demonstrating the effectiveness of the method in suppressing flutter.

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