12.3 : 曲线运动：法向分量和切向分量

When a particle moves along a curved trajectory, its motion can be described using tangential and normal components. Both the components are attached to the particle and move with it.

For the n-axis, the curved path of the particle is split into multiple different arc segments. Each segment forms the arc of a circle having a radius of curvature and a center of curvature.

The n-axis is normal to the t-axis, and its positive sense points towards the center of the curvature, defined with unit vector u_n.

The positive of the t-axis is defined along the increasing position of the particle on the path, and it is denoted using a unit vector, u_t.

The particle's velocity is always tangent to the path of the curvilinear motion and has only a t-component.

Differentiating velocity expression with time gives the acceleration of the particle. Here, u_t changes at each instant, and its change denotes the direction of u_n.

This means that for curvilinear motion, the acceleration of the particle has both tangential and normal components