By Jer-Nan Juang
By Minh Q. Phan
Publisher: Cambridge University Press
Print Publication Year: 2001
Online Publication Date:September 2009
Online ISBN:9780511547119
Hardback ISBN:9780521783552
Paperback ISBN:9780521031905
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511547119.004
Subjects: Engineering design, kinematics, and robotics, Computational Science
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Introduction
In this chapter, methods for developing dynamic equations of motion are introduced. We start with Newton's laws, which are fundamental to dynamic systems. Direct applications of Newton's laws to develop dynamic equations of motion become difficult for dynamic systems with complex configurations such as aircraft, automobiles, etc. D'Alembert's principle is introduced to derive the principle of virtual work for a body composed of a number of particles acted on by a number of external forces. By the concept of virtual work, Hamilton's principle is shown. Hamilton's principle is then used to formulate Lagrange's equation of motion (Refs. [1–2]). In contrast to Newton's second law, which involves vector quantities such as forces and accelerations, Hamilton's principle and Lagrange's equation use scalar quantities, including kinetic energy, potential energy, and virtual work, to develop the system's equations of motion. Along a similar line, Gibbs–Appell equations of motion are introduced with the scalar formed by the squared amplitude of acceleration instead of kinetic and potential energies. Finally, Kane's equations are derived with the same approach used in formulating the Gibbs–Appell equations. Kane's equations introduce a generalized speed vector rather than a scalar quantity (Ref. [3]). All techniques are related. Selecting a method to derive dynamic equations of motion is problem dependent.
Newton's Three Fundamental Laws
These laws were formulated and published by Sir Isaac Newton (1642–1726) in 1687 in his famous Principia (Philosophiae Naturalis Principia Mathematica).
pp. i-vi
pp. vii-xii
pp. xiii-xvi
1 - Ordinary Differential Equations : Read PDF
pp. 1-13
2 - Elementary Matrix Algebra : Read PDF
pp. 14-44
3 - Modeling Techniques : Read PDF
pp. 45-79
4 - Finite-Element Method : Read PDF
pp. 80-119
5 - Response of Dynamic Systems : Read PDF
pp. 120-144
6 - Virtual Passive Controllers : Read PDF
pp. 145-163
7 - State–Space Models : Read PDF
pp. 164-183
8 - State-Feedback Control : Read PDF
pp. 184-216
9 - Dynamic Feedback Controller : Read PDF
pp. 217-255
10 - System Identification : Read PDF
pp. 256-294
11 - Predictive Control : Read PDF
pp. 295-332
pp. 333-334