Each of the Maxwell's equations has both an integral and differential form. Schroedinger's equation is a differential equation and, apparently (I haven't studied it yet), Feynman's path integrals are an equivalent formulation. Newton has got a differential equation $F = \dot p$. Is there an equivalent integral formulation of Newton's law? Would it even be useful if there were?

  • $\begingroup$ Well Newton's formula for gravity is identical to Guass's Law for electrostatics: Poisson's Equation. I only comment because that's not exactly what you are asking about. $\endgroup$
    – Jared
    Mar 23 '15 at 6:20

The impulse momentum theorem would be your best answer:

$p(t) = \int_0^tf(t')dt'$

  • $\begingroup$ I would suggest that the it should be from $t_0$ to $t$ rather than $0$ to $t$--but I'm not sure it matters. $\endgroup$
    – Jared
    Mar 23 '15 at 6:17
  • $\begingroup$ Sure, writing the lower limit as $t_0$ generalises the integral form as this can later be set to 0 or whatever, as necessary. $\endgroup$
    – Dai
    Mar 23 '15 at 6:52
  • 1
    $\begingroup$ Or &p(t) = \int_{t_0}^{t} m(t')a(t') dt$ to be even more general... $\endgroup$
    – Dai
    Mar 23 '15 at 6:54
  • $\begingroup$ @CStarAlgebra can you define your variables? Is $t' = t$? Is $f$ the resultant force, that is $\sum \vec F= m \vec a$? $\endgroup$
    – Armadillo
    May 27 '16 at 13:47

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