作词 : 无
作曲 : DR1N0
Here are some important definitions.
这些是定义。
Displacement:
位移：
R=Re^jθ
All particles of a body move in parallel planes and travel by same distance is known as linear displacement.
物体所有粒子在平行的平面内移动相同距离称为线位移。
A body rotating about a fixed point in such a way that all particles move in circular path is known as angular displacement.
物体和它所有的粒子绕固定点沿圆周路径移动称为角位移。
If we take the first order derivative of the displacement equation, we get:
位移方程对时间求一阶导数得：
d/dt(Re^jθ)=R'e^jθ+Re^(jθ)jθ'=R'e^jθ+Rθ'je^jθ
The angular velocity
角速度
w=dθ/dt.
The linear velocity
线速度
v=dR/dt.
Acceleration, the rate of change of velocity.
加速度是速度的变化率。
Now we take the second order derivative of the displacement equation, we get:
位移方程对时间求二阶导数得：
d^2/dt^2(Re^jθ)=R''e^jθ+R'θ'je^(jθ)+(Rθ''+R'θ')je^jθ+Rθ'je^(jθ)jθ'=R''e^jθ+2θ'R'je^jθ+θ''Rje^jθ-R(θ'^2)e^jθ
The angular acceleration
角加速度
α=θ''=dw/dt
The linear acceleration
线加速度
a=R''=dv/dt
Here's a simple case.
举个栗子。