5d6b8d6d-d1c3-4a9f-8ec7-c2505adf67bb 6 Alvaro Diaz Falconi 4 5 false false 0 0 decimal

ode m t q t 2 diff * m g L / * t q sin * - ≡ (:

Pendulum

ode.a ode t q sin t q equrep :

Small angle solution

t θa ode.a 0 q θo ≡ D\0028\q\0029\\0028\0\0029\ 0 ≡ 31 sys dsolve rhs maple : θo g L * sqrt t * L / cos *

μ ode DEtools[intfactor] maple : t q t diff

Integrating factor and first integral

fi μ ode * DEtools[firint] lhs maple : 2_C1 L * g t q cos * - (* t q t diff 2^L * + 2 L * /

fi DEtools[odeadvisor] maple [_quadrature]

But a hard one ... this is the solution

z k cd z k cn z k dn / :

Jacobi elliptic function cd (using Cephes plugin)

t θ 2 θo 2 / sin g L / sqrt t * θo 2 / sin cd * asin * :

Comparing with the small angle approximation

θo 30 deg * : g g.e : L 5 m * : 31 line

x s * θ x s * θa 2 1 sys

Alvaro

4 appVersion 1.0.8348.30405