Nonlinear Vibrations in Mechanical and Electrical Systems
Presents underlying principles and theories using an easily understood approach. Focuses specifically on those features of the problems in which nonlinearity results in a variety of distinctive new phenomena that can be treated by techniques both interesting and instructive in themselves and which do not require the use of sophisticated mathematics. Recent work discussed includes the endeavors of Levinson and Smith on the existence and uniqueness of the periodic solution in a general case of the self-excited type, Haag and Dorodnitsyn on asymptotic developments and quantities associated with relaxation oscillations. Along with 5 appendices containing rigorous existence and uniqueness proofs, readers are both implicitly and explicitly supplied with hints regarding new problems to be tackled plus numerous ideas and techniques that can be used to solve them.
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Free Vibrations of Undamped Systems with Nonlinear Restoring
Free Oscillations with Damping and the Geometry of Integral Curves
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addition amplitude Appendix applied approximation assumed becomes called Chapter character characteristic circuit closed coefficients combination consider constant contains corresponding course damping defined depends determined differential equation direction discussion Duffing equilibrium example excitation existence external fact field Figure fixed follows force forced oscillations free oscillation frequency function given harmonic oscillations hence important increases indicated initial integral curves interest introduce later lead limit cycle linear means method motion motor negative nonlinear observe obtained occur once origin pendulum periodic solutions positive possible preceding section present problem prove quantity readily regions relation response curves result ring satisfy seen shown simple singularities solution curves spring stable sufficiently tend theory tion torque treated turn unstable values vanish variable vertical vibration yields zero