Newtonian Examples

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

According to Newton’s second law, the acceleration of a particle is proportional to the net force acting on it. In cases, in which the net force depends on the actual position and on the actual velocity of the particle, the system is described by a second-order ODE (due to the velocity and the acceleration being the first and the second derivatives of the position, respectively). In cases, in which the net force depends on both the actual and some delayed values of the particle’s position and velocity, the system is described by a second-order DDE. Second-order systems are therefore often used in engineering to model dynamic behavior. In this chapter, some special second-order scalar DDEs are considered and analyzed by the semidiscretization method.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages73-92
Number of pages20
DOIs
Publication statusPublished - Jan 1 2011

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume178
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Fingerprint

Delay Differential Equations
Second Order ODE
Semidiscretization
Second-order Systems
Second derivative
Dynamic Behavior
Dynamic models
Directly proportional
Scalar
Derivatives
Engineering
Model

Keywords

  • Gray Shading
  • Monodromy Matrix
  • Parameter Plane
  • Stability Boundary
  • Stable Domain

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Insperger, T., & Stépán, G. (2011). Newtonian Examples. In Applied Mathematical Sciences (Switzerland) (pp. 73-92). (Applied Mathematical Sciences (Switzerland); Vol. 178). Springer. https://doi.org/10.1007/978-1-4614-0335-7_4

Newtonian Examples. / Insperger, T.; Stépán, G.

Applied Mathematical Sciences (Switzerland). Springer, 2011. p. 73-92 (Applied Mathematical Sciences (Switzerland); Vol. 178).

Research output: Chapter in Book/Report/Conference proceedingChapter

Insperger, T & Stépán, G 2011, Newtonian Examples. in Applied Mathematical Sciences (Switzerland). Applied Mathematical Sciences (Switzerland), vol. 178, Springer, pp. 73-92. https://doi.org/10.1007/978-1-4614-0335-7_4
Insperger T, Stépán G. Newtonian Examples. In Applied Mathematical Sciences (Switzerland). Springer. 2011. p. 73-92. (Applied Mathematical Sciences (Switzerland)). https://doi.org/10.1007/978-1-4614-0335-7_4
Insperger, T. ; Stépán, G. / Newtonian Examples. Applied Mathematical Sciences (Switzerland). Springer, 2011. pp. 73-92 (Applied Mathematical Sciences (Switzerland)).
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