Mechanics, Second Course

Aim

To develop the knowledge of rigid body dynamics to a level where problems where the motion as a function of time of a rigid body in three dimensions can be analyzed and solved using a computer. After the course, the student should be able to:

• Apply Coriolis equation to formulate the equations of motion and rotational motion in an accelerating and rotating coordinate system.
• Apply some parameterization of the coordinate transformation matrix to transform vectors between coordinate systems and to write relations between orientation and angular velocity for a rigid body.
• Formulate a system of first order differential equations for the motion of a rigid body in a rotating and accelerating coordinate system.
• Implement such differential equations to compute the motion of a rigid body with specified forces and moments on a computer.

Content

Newton's equations of motion, the concept of an inertial system,coordinate transformations, Coriolis' equation, the moment equation,moment of momentum, the inertia tensor, differential-algebraic systems,the Euler angles, the Euler parameters, the strap-down equations,Newton's bucket, gravitational and inertial mass.