lagranians y ecuacions diferencials

(m/2)·d_{t}[x]^{2} = a_{3}·(4/3)·x^{3}+...

... (1/(2m))·( qgt )^{2}+(-1)·(a_{2}/2)·( e^{i·(a_{2}/m)^{(1/2)}·t} )^{2}

x(t) = [[(-2)]]( (-1)·(1/2)·( (2/m)·a_{3}·(4/3) )^{(1/2)}·t , ...

... ( ...

... (1/m^{2})·(qg)^{2}·(1/12)·t^{4}+...

... (1/4)·( e^{i·(a_{2}/m)^{(1/2)}·t} )^{2} ...

... )^{(-1)·(1/4)})

mecánica lineal:

energía:

mc·d_{t}[x(t)] = E_{1}(x)+...+E_{n}(x)

fuerza:

mc·d_{tt}^{2}[x(t)]·(1/d_{t}[x]) = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

mc·d_{tt}^{2}[x(t)] = d_{t}[ E_{1}(x)+...+E_{n}(x) ]

sin momento:

mc != mc·ln( d_{t}[x] )

mecánica clásica:

energía:

(m/2)·d_{t}[x(t)]^{2} = E_{1}(x)+...+E_{n}(x)

fuerza:

m·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

m·d_{tt}^{2}[x(t)]·d_{t}[x(t)] = d_{t}[ E_{1}(x)+...+E_{n}(x) ]

momento:

m·d_{t}[x(t)] = int[ d_{x}[ E_{1}(x)+...+E_{n}(x) ] ] d[t]

mecánica enésima:

energía:

(1/n)·(m/c^{n+(-2)})·d_{t}[x(t)]^{n} = E_{1}(x)+...+E_{n}(x)

fuerza:

(m/c^{n+(-2)})·d_{t}[x(t)]^{n+(-2)}·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

((mc)/c^{n+(-1)})·d_{t}[x(t)]^{n+(-1)}·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

momento:

n != 2 ==>

(m/c^{n+(-2)})·d_{t}[x(t)]^{n+(-1)} != (m/c^{n+(-2)})·(1/(n+(-1)))·d_{t}[x(t)]^{n+(-1)}