Lecture_05 - spinning top equation of motion
Lecture_05 - spinning top equation of motion¶
In this lecture, you use the parallel axis theorem to change the point of rotation for a 3D object. Kinetic energy, \(T\), can be written in 3 ways for a rigid body:
\(T=\frac{1}{2}m\mathbf{v}_G^2+\frac{1}{2}\mathbf{\omega H_G}\)
\(T=\frac{1}{2}\mathbf{\omega H_B}\)
\(T=\frac{1}{2}m\mathbf{v}_B^2+\frac{1}{2}m\mathbf{v}_B\cdot\mathbf{v}_G+\frac{1}{2}\mathbf{\omega H_B}\)
where
\(\mathbf{v}_G\) is the velocity of the center of mass
\(\mathbf{v}_B\) is the velocity any point within a rigid body
\(\mathbf{H}_G\) is the angular momentum around the center of mass
\(\mathbf{H}_B\) is the angular momentum around the point \(B\) within the rigid body
\(\mathbf{\omega}\) is angular velocity of the rigid body
Why are there three different equations? When do you use equations (1), (2), and (3)?
What is an example of an engineering application that you could use a fast-spinning top, when \(\dot{\phi}=\frac{mgd}{I_z\dot{\psi}}\)?