# DSolve to make the path of a ball in a rotating turntable

I have two equations from a analisys of the following situation. A ball starts to move from the center of a turntable (rotating disk). I tried to solve these equations in Mathematica but the solution is too long and complex.

I want to make a ball following the solution of these equations.

eqx = DSolve[{(x''[t] == w^2 x[t] + 2 w Derivative[y][t] + w'[t] (y[t])}, x[t], t]
eqy = DSolve[{(y''[t] ==  w^2 y[t] - 2 w Derivative[x][t] - w'[t] (x[t])}, y[t], t]
CondIni = {x == 0, x' == 0, y == 0, C == 1, C == 1,
K == 1, K == 0}
Exemplo = Join[Equacao, CondIni]


If someone could help with these solutions, or the manipulation of a ball following these equations I'd be grateful..

w[t_] := Cos@t
nd = NDSolveValue[{
x''[t] == w[t]^2 x[t] + 2 w[t] y'[t] + w'[t] y[t],
y''[t] == w[t]^2 y[t] - 2 w[t] x'[t] - w'[t] x[t],
y == 0, y' == 1,
x == 0, x' == 0}, {x, y}, {t, 0, 10}];

ParametricPlot[Through[nd[t]], {t, 0, 10}] Or shorter in vector form:

w[t_] := Cos@t
s = RotationMatrix[-Pi/2];

nd = NDSolveValue[{r''[t] == {r[t], s.r'[t], s.r[t]}.{w[t]^2, 2 w[t], w'[t]},
r == {0, 0}, r' == {0, 1}}, {r}, {t, 0, 10}];

ParametricPlot[Through[nd[t]], {t, 0, 10}]

• It works... I´ll try to make a manipulate follow this path, theres is a way to make an object, like a ball, follow the path? – dcvilela Feb 23 '16 at 18:46
• @dcvilela Your previous question was about that! – Dr. belisarius Feb 23 '16 at 18:58
• Yeah... thats what i´m trying!! – dcvilela Feb 23 '16 at 19:01