Lecture 4 Visualization and Animation 1 Use Mathematica

Lecture 4 Visualization and Animation 1

Use Mathematica to visualize the motion of physical systems 2

Simple examples n

Parametric equations n 4

Examples of parametric equations n

Derivation of the equation of motion for SHO Force on the pendulum for small oscillation, Equation of motion (Eo. M) l r

Animation of simple pendulum 7

Examples of parametric equations: n projectile motion 2 D

Animation of 2 D projectile 10

Examples of parametric equations: 2 -body Planetary motion a b C(h, k) n

Animation of planetary orbital motion 12

Assignments n

1 D sinusoidal wave n 14

1 D sinusoidal wave n 15

1 D sinusoidal wave n 16

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Adding two 1 D sinusoidal waves n 18

Animation exercises

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Animation of wavepulse 23

2 D radially symmetric wave n 24

Animation assignment Animate an radially outgoing 2 D sinusoidal wave To visualize it, use List. Density. Plot[ ] You may need to impose the option Interpolation. Order -> 0 in List. Density. Plot[ ]

Sun-Earth-Moon planetary motion n a b C(h, k) 26

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Simplified Sun-Earth-Moon threebody planetary motion n a b C(h, k) 28

Animation of three-body planetary motion

Assignment: oscillating string Simulate the oscillating string as shown. 30

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Example of a periodic function with Mathematica using Module n 32

Exercise n 33

Lissajous pattern https: //en. wikipedia. org/wiki/Lissajous_curve n 34

Animation of Lissajous pattern 35