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--- book:chap6:lagrange [2021/10/07 05:17] – jv
+++ book:chap6:lagrange [2022/02/14 14:05] (current) – abril
@@ Line 1: / Line 1: @@
 ====== 6. Integrable Dynamics ======
+<WRAP right #fig_girl-on-swing 115pt>
+{{girl-on-swing.png}}
+[[https://commons.wikimedia.org/wiki/File:Sketch_by_Marguerite_Martyn_of_a_girl_standing_on_a_swing_in_a_bathing_suit_getting_dry_from_the_breeze,_1914.png}{wikimedia/public domain | Marguerite Martyn, 1914]]\\
+Figure 6.1: The point-particle idealization of a girl on a swing is the mathematical pendulum of Figures 1.2 and 1.3.
+</WRAP>
+In [[book:chap5:spatial-extension|Chapter 5]] we considered objects that consist of a mass points
+with fixed relative positions, like a flying and spinning ping-pong
+ball. Rather than providing a description of each individual mass
+element, we established equations of motion for their center of mass
+and the orientation of the body in space. From the perspective of
+theoretical mechanics the fixing of relative positions is a constraint
+to their motion, just as the ropes of a swing enforces a motion on
+a one-dimensional circular track, rather than in two dimensions.
+The deflection angle θ of the pendulum, and the center of mass and
+orientation of the ball are examples of generalized coordinates that
+automatically take into account the constraints.\\
+In this chapter we discuss how to set up generalized coordinates
+and how to find the associated equations of motion. The discussion
+will be driven by examples. The examples will be derived from the
+realm of integrable dynamics. These are systems where conservation laws can be used to break down the dynamics into separate problems that can be interpreted as motion with a single degree of freedom.\\
+At the end of the chapter you know why coins run away rolling
+on their edge, and how the speed of a steam engine was controlled
+by a mechanical device. Systems where the dynamics is not integrable will subsequently be addressed in Chapter 7.
+----
+  * [[ 6.1 Motivation and Outline |6.1 Motivation and Outline: How to deal with constraint motion?]]
+  * [[ 6.2 Lagrange formalism |6.2 Lagrange formalism]]
+  * [[ 6.3 Dynamics with one degree of freedom |6.3 Dynamics with one degree of freedom]]
+  * [[ 6.4 Several DOF and conservation laws |6.4 Several degrees of freedom and conservation laws]]
+  * [[ 6.5 Dynamics of 2-particle systems |6.5 Dynamics of 2-particle systems]]
+  * [[ 6.6 Worked problems |6.6 Worked problems: spinning top and running wheel]]
+  * [[ 6.7 Problems |6.7 Problems]]
+~~DISCUSSION~~
 The PDF file of the chapter is available  {{ book:chap6:2021_jv_unil_mechanics_chap06.pdf |here}}.