Kirjahaku

In his great work, Mecanique Analytique (1788)-^Lagrange used the term "analytical" to mean "non-geometrical." Indeed, Lagrange made the following boast: "No diagrams will be found in this work. The methods that I explain in it require neither constructions nor geometrical or mechanical arguments, but only the algebraic operations inherent to a regular and uniform process. Those who love Analysis will, with joy, see mechanics become a new branch of it and will be grateful to me for thus having extended its field." This was in marked contrast to Newton's Philosohiae Naturalis Principia Mathematica (1687) which is full of elaborate geometrical constructions. It has been remarked that the classical Greeks would have understood some of the Principia but none of the Mecanique Analytique. The term analytical dynamics has now come to mean the develop­ ments in dynamics from just after Newton to just before the advent of relativity theory and quantum mechanics, and it is this meaning of the term that is meant here. Frequent use will be made of diagrams to illus­ trate the theory and its applications, although it will be noted that as the book progresses and the material gets "more analytical", the number of figures per chapter tends to decrease, although not monotonically.

Most books on this subject are designed for elective courses in "intermediate dynamics" covering advanced Newtonian and introductory Lagrangian methods. Such books do not give adequate emphasis to advanced topics in Newton-Euler dynamics. Because the first required course in dynamics usually concentrates on 2-D dynamics, important 3-D problems are left to a further course. Examples are robots, automated manufacturing devices, aerospace vehicles, and biomechanical components. This material cannot be covered adequately in one course if it is to be shared with an introduction to Langrangian methods. This text is devoted to application of Newton-Euler methods to complex, real-life 3-D dynamics problems; it essentially completes this topic.

Most books on this subject are designed for elective courses in "intermediate dynamics" covering advanced Newtonian and introductory Lagrangian methods. Such books do not give adequate emphasis to advanced topics in Newton-Euler dynamics. Because the first required course in dynamics usually concentrates on 2-D dynamics, important 3-D problems are left to a further course. Examples are robots, automated manufacturing devices, aerospace vehicles, and biomechanical components. This material cannot be covered adequately in one course if it is to be shared with an introduction to Langrangian methods. This text is devoted to application of Newton-Euler methods to complex, real-life 3-D dynamics problems; it essentially completes this topic.