TY - CHAP
T1 - Introduction to Analytical Mechanics
AU - Mottaghi, Sohrob
AU - Gabbai, Rene
AU - Benaroya, Haym
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrange’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 Hamilton’s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrange’s equation. Hamilton’s principle 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 Lagrange’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 Hamilton’s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrange’s equation. Hamilton’s principle 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 -