### 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 language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 73-92 |

Number of pages | 20 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
---|---|

Volume | 178 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Newtonian Examples

AU - Insperger, T.

AU - Stépán, G.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Gray Shading

KW - Monodromy Matrix

KW - Parameter Plane

KW - Stability Boundary

KW - Stable Domain

UR - http://www.scopus.com/inward/record.url?scp=85068174730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068174730&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-0335-7_4

DO - 10.1007/978-1-4614-0335-7_4

M3 - Chapter

T3 - Applied Mathematical Sciences (Switzerland)

SP - 73

EP - 92

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -