doc(kepler-problem): #82 add tutorial

[emptymalei]

Resolves #82

• from_geometry: multiple examples to show case the different orbits
  • circular orbit
  • ellipse
  • hyperbolic
  • parabolic
• use iom
• Maybe some explanations on how the equation was solved.

[github-actions]

Coverage Report (54749d5, 3.12, macos-latest)

File	Stmts	Miss	Cover	Missing
hamilflow
__init__.py	0	0	100%
hamilflow/maths
__init__.py	2	0	100%
trigonometrics.py	13	2	2	85%
hamilflow/models
__init__.py	0	0	100%
brownian_motion.py	49	2	2	96%
free_particle.py	38	2	2	95%
harmonic_oscillator.py	115	10	10	91%
harmonic_oscillator_chain.py	46	7	7	85%
pendulum.py	60	2	2	97%
hamilflow/models/kepler_problem
__init__.py	2	0	100%
dynamics.py	61	2	2	97%
model.py	127	11	11	91%
numerics.py	59	11	11	81%
hamilflow/models/utils
__init__.py	0	0	100%
typing.py	4	0	100%
TOTAL	576	49	91%

Tests	Skipped	Failures	Errors	Time
2642	22 💤	0 ❌	0 🔥	9.939s ⏱️

[github-actions]

PR Preview Action v1.4.7
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2024-09-25 06:59 UTC

[cmp0xff]

The tutorial shows the trajectory, which is solved by the textbook Kepler problem. However, it does not show our strength in that the trajectory is parameterised by time. For example, can we use colour to indicate the speed?

[emptymalei]

The tutorial shows the trajectory, which is solved by the textbook Kepler problem. However, it does not show our strength in that the trajectory is parameterised by time. For example, can we use colour to indicate the speed?

good point. I added some animations.

[cmp0xff]

The tutorial shows the basics and our strengths. I can approve it after this round of review.

• We need to fix the floating error when displaying t. Currently we see weird numbers like -3.299999999, -3.199999999, -3.1, etc. If I were writing the code, I would divide 1 by a power of 2.
• We can to make the animations more impressive.
  • We need to make them smoother.
  • For periodic orbits, we can do fewer revolutions.
  • For unbounded motion, we should somehow emphasise that the motion near the vertex is faster.