mecànica clàssica arrel cúbica de la posició

m·d_{t}[x(t)] = a·( x(t) )^{(1/3)}


m·d_{tt}^{2}[x(t)] = (1/3)·a·( x(t) )^{(-1)(2/3)}·d_{t}[x(t)]


m·d_{tt}^{2}[x(t)] = (1/3)·(a^{2}/m)·( x(t) )^{(-1)(1/3)}


( x(t) )^{(1/3)}·d_{tt}^{2}[x(t)] = (1/3)·(a^{2}/m^{2})


d_{t}[x(t)]·d_{tt}^{2}[x(t)] = (1/3)·(a^{3}/m^{3})


(1/2)·d_{t}[x(t)]^{2} = (1/3)·(a^{3}/m^{3})·t


d_{t}[x(t)] = ( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(1/2)}


x(t) = ( (2/3)·(a/m) )^{(3/2)}·t^{(3/2)}


d_{tt}^{2}[x(t)] = (1/2)·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(-1)(1/2)}


E(t) = ∫ [ (m/2)·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(-1)(1/2)}·( (2/3)·(a^{3}/m^{3}) )^{(1/2)}·t^{(1/2)}) ] d[t]
E(t) = ∫ [ (m/2)·( (2/3)·(a^{3}/m^{3}) ) ] d[t]


E(t) = (1/3)·(a^{3}/m^{2})·t


(m/2)·d_{t}[x(t)]^{2} = (1/3)·(a^{3}/m^{2})·t