Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

2001 ◽  
Author(s):  
Thomas H. Kerr III
Keyword(s):  
Linear System ◽  
Closed Form ◽  
System Software ◽  
Testing Linear

Normal Modes of Nonlinear Dual-Mode Systems

1960 ◽  
Vol 27 (2) ◽  
pp. 263-268 ◽  
Author(s):  
R. M. Rosenberg
Keyword(s):  
Linear System ◽  
Closed Form ◽  
Normal Modes ◽  
Coupled System ◽  
Dual Mode ◽  
Great Simplicity

A system consisting of two unequal masses, interconnected by a coupling spring, and each connected to an anchor spring, is examined. The springs may all be unequal and nonlinear, but each resists being compressed to the same degree as being stretched. The concept of normal modes is rigorously defined, and methods of finding them are given. A knowledge of these modes reduces the coupled system to two uncoupled ones which can always be integrated in quadrature. There exists an infinity of systems, of which the linear is one, which can be integrated in closed form. This approach yields, even for the linear system, new results of great simplicity.

Linear Waves in Bubbly Liquids via the Kramers-Kronig Relations

1991 ◽  
Vol 113 (3) ◽  
pp. 417-419
Author(s):  
N. Brauner ◽  
A. I. Beltzer
Keyword(s):  
Linear System ◽  
Closed Form ◽  
Acoustic Waves ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Bubbly Liquids ◽  
Linear Waves ◽  
Causal Approach ◽  
Effective Wave ◽  
Arbitrary Frequency

A simple closed form analytic solution, as well as numerical solutions, are derived for acoustic waves of an arbitrary frequency, propagating in dilute bubbly liquids. The applied method treats the effective wave as a causal response of a linear system. The results are compared with the prediction of Foldy’s theory, which in this particular case is shown to be consistent with the Kramers-Kronig relations. These results thus complement recently reported investigations concerning the causal approach as well as the validity of Foldy’s theory.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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