book:chap4:eom-ode
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====== 4. Motion of Point Particles ====== | ====== 4. Motion of Point Particles ====== | ||
- | The PDF file of the chapter | + | In [[book: |
+ | finding the forces acting on a body, | ||
+ | and thus determining the acceleration | ||
+ | For a particle of mass~$m$ and position~$\vec q$ | ||
+ | Newton' | ||
+ | to the force that is acting on the particle. | ||
+ | In [[book: | ||
+ | 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 | + | <WRAP center 330pt> |
+ | {{Planetarium_in_Putnam_Gallery_2, | ||
+ | Mechanical planetarium used to teach astronomy at Harvard | ||
+ | [[https:// | ||
+ | [[https:// | ||
+ | </ | ||
+ | |||
+ | 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 ' | ||
+ | |||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | |||
+ | * [[ 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 | ||
~~DISCUSSION~~ | ~~DISCUSSION~~ |
book/chap4/eom-ode.1610702066.txt.gz · Last modified: 2021/01/15 10:14 by 3725327