# DrifterFun

One need not hope in order to undertake, nor succeed in order to persevere.

# 恒定功率启动问题

### 2018-04-11

$$a:加速度; f:摩擦力; P:功率; v:速度; t:时间; x:位移;$$

$$my\frac{dy}{dx}+fy=P$$ $$mydy+fydx=Pdx$$ $$mydy = (P-fy)dx$$ $$\frac{my}{P-fy}dy=dx$$ $$(-\frac{m}{f}+\frac{\frac{mP}{f}}{P-fy})dy=dx$$ $$-\frac{m}{f}y+\frac{mP}{f}\int(P-fy)dy=x$$ $$-\frac{m}{f}y-\frac{mP}{f^2}\int(P-fy)d(P-fy)=x$$ $$-\frac{m}{f}y-\frac{mP}{f^2}ln(P-fy)=x$$

$$其中v为瞬时速度; C_0=\frac{mP}{f^2}ln(P) （由v=0时x=0得到）$$