docs: update readme (#354)

Signed-off-by: nstarman <nstarman@users.noreply.github.com>

README.md

@@ -1,16 +1,88 @@
-# galax
+<h1 align='center'> galax </h1>
+<h2 align="center">Galactic and Gravitational Dynamics</h2>
 
-[![Actions Status][actions-badge]][actions-link]
-[![Code Coverage][codecov-badge]][codecov-link]
-[![Documentation Status][rtd-badge]][rtd-link]
+## Installation
 
-[![PyPI version][pypi-version]][pypi-link]
-[![Conda-Forge][conda-badge]][conda-link]
 [![PyPI platforms][pypi-platforms]][pypi-link]
+[![PyPI version][pypi-version]][pypi-link]
+
+<!-- [![Conda-Forge][conda-badge]][conda-link] -->
+
+```bash
+pip install galax
+```
+
+## Documentation
+
+[![Documentation Status][rtd-badge]][rtd-link]
+
+Coming soon. In the meantime, if you've used `gala`, then `galax` should be
+familiar!
+
+## Quick example
+
+Let's compute an orbit!
+
+```python
+import coordinax as cx
+import galax.coordinates as gc
+import galax.dynamics as gd
+import galax.potential as gp
+import jax.numpy as jnp
+from unxt import Quantity
+
+w = gc.PhaseSpacePosition(
+    q=Quantity([8, 0, 0], "kpc"),
+    p=Quantity([0, 220, 0], "km/s"),
+    t=Quantity(0, "Myr"),
+)
+
+pot = gp.MilkyWayPotential()
+
+orbit = gd.evaluate_orbit(pot, w, Quantity(jnp.linspace(0, 1, 100), "Gyr"))
+print(orbit)
+# Orbit(
+#     q=<CartesianPosition3D (x[kpc], y[kpc], z[kpc])
+#         [[ 8.     0.     0.   ]
+#          ...
+#          [ 7.804 -0.106  0.   ]]>,
+#     p=<CartesianVelocity3D (d_x[kpc / Myr], d_y[kpc / Myr], d_z[kpc / Myr])
+#         [[ 0.     0.225  0.   ]
+#          ...
+#          [ 0.018  0.23   0.   ]]>,
+#     t=Quantity['time'](Array([0., ..., 1000.], dtype=float64), unit='Myr'),
+#     potential=MilkyWayPotential(...)
+# )
+
+orbit_sph = orbit.represent_as(cx.LonLatSphericalPosition)
+print(orbit_sph)
+# Orbit(
+#     q=<LonLatSphericalPosition (lon[rad], lat[deg], distance[kpc])
+#         [[0.000e+00 3.858e-16 8.000e+00]
+#          ...
+#          [6.270e+00 3.858e-16 7.805e+00]]>,
+#     p=<LonLatSphericalVelocity (d_lon[rad / Myr], d_lat[deg / Myr], d_distance[kpc / Myr])
+#         [[ 0.028  0.     0.   ]
+#          ...
+#          [ 0.03   0.     0.015]]>,
+#     t=Quantity['time'](Array([0., ..., 1000.], dtype=float64), unit='Myr'),
+#     potential=MilkyWayPotential(...})
+# )
+```
+
+## Citation
+
+[![DOI][zenodo-badge]][zenodo-link]
+
+If you found this library to be useful in academic work, then please cite.
+
+## Development
+
+[![Actions Status][actions-badge]][actions-link]
 
-[![GitHub Discussion][github-discussions-badge]][github-discussions-link]
+We welcome contributions!
 
-## Contributors
+### Contributors
 
 See the
 [AUTHORS.rst](https://github.com/GalacticDynamics/galax/blob/main/AUTHORS.rst)
@@ -38,5 +110,7 @@ this package would have had a worse name.
 [pypi-version]:             https://img.shields.io/pypi/v/galax
 [rtd-badge]:                https://readthedocs.org/projects/galax/badge/?version=latest
 [rtd-link]:                 https://galax.readthedocs.io/en/latest/?badge=latest
+[zenodo-badge]:             https://zenodo.org/badge/706347349.svg
+[zenodo-link]:              https://zenodo.org/doi/10.5281/zenodo.11553324
 
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