13.5 :  중앙군 운동

The central force system involves a force acting on an object towards a fixed point, typically the origin. This force is determined by the object's distance from the fixed point.

If the mass of the object is 'm', polar coordinates are used to describe the equation of motion. 

The azimuthal component of force is zero. Rewriting this equation and integrating it shows that the product of the radial distance squared with angular velocity is constant.

As the object displaces by the angular displacement dθ, it describes an area dA. It means that the areal velocity of the object is a constant.

So, the first and the second time derivatives of radial component can be written using the chain rule of differentiation and the object's areal velocity.

Here, a new dependent variable is defined that simplifies the radial and angular components of the equation of motion.

Substituting radial and angular velocity components in the equation of motion gives the equation for the path of the motion for the object under the central force.