Concepedia

Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds

S. C. Sinha, Sangram Redkar, Eric A. Butcher

Journal of Sound and Vibration · 2004 · 41 citations · 13 references

Concepts

Natural SciencesMathematicsSystems EngineeringDifferential EquationsDynamical SystemsCanonical TransformationsControl TheoryInvariant ManifoldsNonlinear ControlNonlinear DynamicsSystems Of Differential EquationsInvariant Manifold ReductionInvariant Manifold TheoremsInvariant Manifolds For Delay Differential EquationsInvariant Manifolds In Partial Differential EquationsInvariant Manifolds Of Periodic OrbitsLocal Invariant ManifoldsModel Order ReductionNonlinear Systems

References

13

Reduction of stiffness and mass matrices

R. J. Guyan · AIAA Journal · 1965 · 2.6K citations · Full text

Engineering, Materials Science, Applied Mechanics +4

1985 IEEE conference on decision and control

IEEE Control Systems Magazine · 1985 · 964 citations

Business, Computer Science, Electrical Engineering +10

Non-linear normal modes and invariant manifolds

Steven W. Shaw, Christophe Pierre · Journal of Sound and Vibration · 1991 · 357 citations · Full text

Natural Sciences, Mathematics, Dynamical Systems +12

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Alexander F. Vakakis · Mechanical Systems and Signal Processing · 1997 · 280 citations · Full text

Engineering, Mechanical Engineering, Physics +16

On the Parametric Excitation of a Dynamic System Having Multiple Degrees of Freedom

C. S. Hsu · Journal of Applied Mechanics · 1963 · 271 citations

Natural Sciences, Mathematics, Differential Equations +13