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--- book:chap4:eom-ode [2021/10/07 05:16] – jv
+++ book:chap4:eom-ode [2021/12/18 12:48] (current) – abril
@@ Line 1: / Line 1: @@
 ====== 4. Motion of Point Particles ======
-The PDF file of the chapter is available  {{ book:chap4:2021_jv_unil_mechanics_chap04.pdf |here}}.
+In [[book:chap3:newton |Chapter 3]] we learned how to set up a physical model based on
+finding the forces acting on a body,
+and thus determining the acceleration of its motion.
+For a particle of mass~$m$ and position~$\vec q$
+Newton's second law relates its acceleration $\ddot{\vec q}$
+to the force that is acting on the particle.
+In [[book:chap2:forcestorques|Chapter 2]] we saw
+that the total force $\vec F( \vec q, \dot{\vec q}, t )$
+acting on the particle may depend on $\vec q$, $\dot{\vec q}$, and $t$.
+The resulting relation between the acceleration and the force is called
+equation of motion of the particle, [[book:chap3:3.3_newton_s_axioms_and_equations_of_motion_eom #EOM |Definition 3.3]]. In the present chapter we will discuss approaches
+that will allow us to systematically find the solutions of EOMs. Moreover, we will explore what type of behavior is encountered for different types of initial conditions.
-I am curious to see your questions, remarks and suggestions:
+<WRAP center 330pt>
+{{Planetarium_in_Putnam_Gallery_2,_2009-11-24.jpg}}
+Mechanical planetarium used to teach astronomy at Harvard
+[[https://commons.wikimedia.org/wiki/File:Planetarium_in_Putnam_Gallery_2,_2009-11-24.jpg |Sage Ross/wikimedia]],
+[[https://creativecommons.org/licenses/by-sa/3.0 |CC BY-SA 3.0]]
+</WRAP>
+At the end of this chapter we will discuss the motion of planets around the sun,
+moons around their planets, and will be able to figure out which rules determine the intricate trajectory of 'Oumuamua shown in [[book:chap3:3.6_problems #fig_Oumuamua-skypath|Figure 3.12]].
+----
+  * [[  4.1 Motivation and outline | 4.1 Motivation and outline: EOM are ODEs]]
+  * [[  4.2 Integrating ODEs | 4.2 Integrating ODEs — Free flight]]
+  * [[  4.3 Separation of variables | 4.3 Separation of variables — Settling with Stokes drag]]
+  * [[  4.4 Worked example_ Free flight | 4.4 Worked example: Free flight with turbulent friction]]
+  * [[  4.5 Linear ODEs | 4.5 Linear ODEs — Particle suspended from a spring]]
+  * [[  4.6 The center of mass (CM) inertial frame | 4.6 The center of mass (CM) inertial frame]]
+  * [[  4.7 Worked example the Kepler problem | 4.7 Worked example: the Kepler problem]]
+  * [[  4.8 Mechanical similarity — Kepler’s 3rd Law | 4.8 Mechanical similarity]]
+  * [[  4.9 Solving ODEs by coordinate transformations | 4.9 Solving ODEs by coordinate transformations — Kepler’s 1st law]]
+  * [[  4.10 Problems | 4.10 Problems]]
+  * [[  4.11 Further reading | 4.11 Further reading]]
+The PDF file of the chapter is available  {{ book:chap4:2021_jv_unil_mechanics_chap04.pdf |here}}.
 ~~DISCUSSION~~