Physics 212x

Harrison Hartle

**
****
**In the original form of classical mechanics developed by
Isaac Newton, the dynamics of objects was modeled primarily by
making a large simplification: treating objects as point
particles with no spatial extent. This is a viable assumption
for modeling many systems such as the dynamics of planetary
bodies. However, when attempting to understand the rotational
and translational motion of objects of size comparable to the
distances of their movements, the point particle model fails.
In cases where the relative configuration of an object’s
makeup is fixed, that object is called a rigid body and the
mechanics governing it’s motion are called rigid body dynamics**.
**

A** **rigid body has a fixed internal configuration of
particles, continuously distributed. A rigid body has six
degrees of freedom: three dimensions of translation and three
angles of rotation. The complete orientation of a rigid body
can be specified by those six numbers. A number of issues need
to be addressed in order to model the motion of extended
objects, in describing the angular orientation of the body,
choosing a convenient reference frame, and modeling the
object’s moment of inertia in three dimensions. Some of the
basic techniques for addressing these issues are discussed
here.

Moment of Inertia, Principal Moments of Inertia, Inertia Tensor

Relationships Between Vectors in Inertial and Rotating Frames

Derivation of Euler's Equations

Bibliography