Transport Theorem Worked Examples - Vector Derivatives When Frames Are Rotating and Translating

Explore vector derivatives in rotating and translating frames through worked examples in this comprehensive lecture on the Transport Theorem. Delve into vector manipulation review, the matrix representation of cross-products, and the tilde matrix. Learn the Transport Theorem for vector derivatives in rotating frames and apply it to real-world scenarios, including a cannon viewed from a rotating frame and oscillatory motion. Work through a detailed turntable example and examine the Transport Theorem's application to Earth's rotation. Conclude with an extension of the theorem to frames that are both rotating and translating, gaining valuable insights into space vehicle dynamics and coordinate frame transformations.

Review of vector manipulations.
matrix way to write cross-product, and the tilde matrix.
Transport Theorem for vector derivatives (transport equation).
Example using cannon seen in rotating frame.
Oscillatory motion seen in rotating frame.
Turntable worked example of vector derivative.
Example of transport theorem for rotating Earth.
Transport theorem for frames that are translating and rotating .