parametric_interact.sagews

%auto
typeset_mode(True, display=False)
curve(t,a,vx,vy,r,w) = [vx*t-r*cos(w*t), r*sin(w*t)-a*t^2/2 + vy*t]

@interact
def parametric(F = input_box(default=10, label='$\\frac{w}{2\pi}$: '), \
               R = input_box(default=0.1, label='$r$: '), \
               V = input_box(default=9, label='$||v||$: '), \
               THETA = input_box(default=70, label='$\\theta \; [{}^\circ]$: '), \
               axis = selector(["x","t"], label='axis', nrows=1, ncols=2, buttons=True)):
    W = 2*pi*F
    A = 10
    Vx = V*cos(THETA*pi/180)
    Vy = V*sin(THETA*pi/180)
    c = curve(a=A,vx=Vx,vy=Vy,r=R,w=W)
    T = c[1].find_root(V/A,2*V/A)

    vx = var ('v_x', latex_name="v_{x}")
    vy = var ('v_y', latex_name="v_{y}")
    pretty_print(curve.subs(vx=vx,vy=vy))
    pretty_print(LatexExpr('$t \; \in \; (0,{})$'.format(T)))
    
    if axis == 'x':
        p = [parametric_plot (c, (t,0,T)), parametric_plot(curve(a=A,vx=Vx,vy=Vy,r=0,w=0),(t,0,T),linestyle='--',color='red')]
    elif axis == 't':
        p = [plot (c[1], (t,0,T)), plot(curve(a=A,vx=Vx,vy=Vy,r=0,w=0)[1],(t,0,T),linestyle='--',color='red')]
    show(sum(p))

Interact: please open in CoCalc