# The Rigid Body Lagrangian and the Inertia Tensor

## There’s more to the world than point particles.

Up to this point in the series, we’ve covered models for the motion of particles, gravity, electromagnetism, waves, heat, and light. While we’ve certainly done a lot, we still have an omission so glaring that we couldn’t even model most objects in our world.

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Most physical objects that you could touch kind of work like particles, but have some extent in space. While we could model these objects as collections of individual points (and we usually have to for soft-bodies), many objects are rigid — they don’t noticeably stretch or squish in any way. These objects are called **rigid bodies**. In this article, we’ll come up with a precise mathematical model for rigid bodies, derive the form of the Lagrangian, and set ourselves up to derive Euler’s Rigid Body Equations.

# Check Your Understanding

We’re going to once again have some standard proofs, derivations, calculations, and Physical modeling. I’ve also put deriving Euler’s Rigid Body Equations from the facts in this article into the mix.