### Abstract

This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrangeâ€™s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamiltonâ€™s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrangeâ€™s equation. Hamiltonâ€™s principleÂ is, especially, relevant to the work in Chaps. 4 and 5.

Original language | English (US) |
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Title of host publication | Solid Mechanics and its Applications |

Publisher | Springer Verlag |

Pages | 57-73 |

Number of pages | 17 |

DOIs | |

State | Published - Jan 1 2020 |

### Publication series

Name | Solid Mechanics and its Applications |
---|---|

Volume | 260 |

ISSN (Print) | 0925-0042 |

ISSN (Electronic) | 2214-7764 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Civil and Structural Engineering
- Automotive Engineering
- Aerospace Engineering
- Acoustics and Ultrasonics
- Mechanical Engineering

### Cite this

*Solid Mechanics and its Applications*(pp. 57-73). (Solid Mechanics and its Applications; Vol. 260). Springer Verlag. https://doi.org/10.1007/978-3-030-26133-7_3

}

*Solid Mechanics and its Applications.*Solid Mechanics and its Applications, vol. 260, Springer Verlag, pp. 57-73. https://doi.org/10.1007/978-3-030-26133-7_3

**Introduction to Analytical Mechanics.** / Mottaghi, Sohrob; Gabbai, Rene; Benaroya, Haym.

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

TY - CHAP

T1 - Introduction to Analytical Mechanics

AU - Mottaghi, Sohrob

AU - Gabbai, Rene

AU - Benaroya, Haym

PY - 2020/1/1

Y1 - 2020/1/1

N2 - This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrangeâ€™s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamiltonâ€™s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrangeâ€™s equation. Hamiltonâ€™s principleÂ is, especially, relevant to the work in Chaps. 4 and 5.

AB - This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrangeâ€™s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamiltonâ€™s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrangeâ€™s equation. Hamiltonâ€™s principleÂ is, especially, relevant to the work in Chaps. 4 and 5.

UR - http://www.scopus.com/inward/record.url?scp=85071495970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071495970&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-26133-7_3

DO - 10.1007/978-3-030-26133-7_3

M3 - Chapter

AN - SCOPUS:85071495970

T3 - Solid Mechanics and its Applications

SP - 57

EP - 73

BT - Solid Mechanics and its Applications

PB - Springer Verlag

ER -