13.1 : 运动方程：直角坐标和柱坐标

For a particle moving relative to an inertial frame, the equation of motion can be written using rectangular components. If motion is restricted to the x-y plane, only the first two equations apply.

Conversely, the equation of motion for a particle moving along a known curved path can be formulated in cylindrical components: radial, azimuthal, and axial, along respective unit vector directions.

The axial direction is perpendicular to the plane formed by the radial and azimuthal directions.

Here, the force along each component gives the acceleration along that particular component.

The acceleration of the particle along the radial component is the difference between the acceleration of the particle along the radial directions and the product of the radius and angular velocity squared.

The acceleration along the azimuthal component is the sum of the product of radius and angular acceleration and the product of the radial and angular velocity.

The acceleration along the axial direction corresponds to the change in speed of the particle along the vertical axis of the cylindrical system.