空气阻力对炮弹的影响

def trajectory3d(theta,phi,speed=20,height=0,dt=0.01,g=-9.81,elevation=flat_ground,drag=0):
    vx = speed * cos(pi * theta / 180) * cos(pi * phi / 180)
    vy = speed * cos(pi * theta / 180) * sin(pi * phi / 180)
    vz = speed * sin(pi * theta / 180)
    t,x,y,z = 0, 0, 0, height
    ts, xs, ys, zs = [t], [x], [y], [z]
    while z >= elevation(x,y):
        t += dt
        vx -= (drag * vx) * dt
        vy -= (drag * vy) * dt
        vz += (g - (drag * vz)) * dt
        x += vx * dt
        y += vy * dt
        z += vz * dt
        ts.append(t)
        xs.append(x)
        ys.append(y)
        zs.append(z)
    return ts, xs, ys, zs