Free Oscillations

  • Frank C. Hoppensteadt
Part of the Applied Mathematical Sciences book series (AMS, volume 94)


A distinction is usually made between systems that are isolated, known as free systems, and those that interact with the outside world, known as forced systems. Often we reduce forced systems to (apparently) free ones by looking at the system stroboscopically or by introducing extra variables to describe external influences. Often we reduce free problems to ones that appear to be forced. For example, systems in which energy is conserved can have dissipative components within them, which can be uncovered by finding a timelike variable among the variables of the system and using it to reduce the problem to a dissipative one of lower order.


Periodic Solution Hamiltonian System Phase Portrait Rotation Number Phase Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  1. 1.College of Natural SciencesMichigan State UniversityEast LansingUSA

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