Projectile transverse motion and stability in electromagnetic induction launchers

The transverse motion of a projectile in an electromagnetic induction launcher is considered. The equations of motion for translation and rotation are derived assuming a rigid projectile and a flyway restoring force per unit length that is proportional to the local displacement. Linearized transverse forces and torques due to energized coils are derived for displaced or tilted armature elements based on a first order perturbation method. The resulting equations of motion for a rigid projectile composed of multiple elements in a multi-coil launcher are analyzed as a coupled oscillator system of equations and a simple linear stability condition is derived. The equations of motion are incorporated into the 2-D Slingshot circuit code and numerical solutions for the transverse motion are obtained.<>