Related Experiment Videos
Newton's laws of motion in the form of a Riccati equation
Marek Nowakowski1, Haret C Rosu
1Instituto de Física de la Universidad de Guanajuato, Apartado Postal E-143, León, Guanajuato, Mexico.
Abstract:
We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.
Related Concept Videos
First Law: Particles in One-dimensional Equilibrium
Newton's Law of Motion
The first law of motion, also known as the law of inertia, states that an object at rest will stay at rest, and an object in motion will continue to move at a constant speed and direction unless acted upon by an external force.
Equation of Motion for a Rigid Body
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
Newton's First Law: Introduction
Equation of Rotational Dynamics