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N-body Systems with Linear Wind Resistance: Analytic Solutions
Joseph West
The attractive and repulsive linear Hookean form of gravity is known to allow for analytic solutions to N-body systems for arbitrary masses and initial conditions. This linear syst…
Analytic Harmonic Tunable Closed Orbits of Trapped N-Body Systems
Joseph West
The motion of each particle in an N body system of identical masses interacting via an attractive or repulsive pairwise linear force law, the "Swarm," and with an external attracti…
N-body linear force law allowing analytic solutions
Joseph West, Sean P. Bartz
We present a pair-wise force law in a system of N particles that produces analytic solutions for arbitrary number of particles, masses, and initial conditions. Each pair of particl…
The ZK Spiral Family of Trajectories and Forces
Joseph West
Particle trajectories in the form of a logarithmic spiral with specified angular time dependence, "ZK spirals," are shown to be analytic solutions for motion in non-central, but si…
Blackbody Friction: Analytic expressions for velocity and position
Joseph West
The equations of motion are solved analytically for speed and position for the case of blackbody friction on objects traveling at relativistic speeds with respect to observers fixe…