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。
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。
