d t ∂ L ∂ θ ˙ − ∂ L ∂ θ = 0 ⇒ l θ ¨ − l ϕ ˙ 2 sin θ cos θ + g sin θ = 0 , d d t ∂ L ∂ ϕ ˙ − ∂ L ∂ ϕ = 0 ⇒ d d t ( m l 2 ϕ ˙ sin 2 θ ) = 0. {\displaystyle
θ {\displaystyle \cos \phi \cos \theta \,} : tg ( ϕ + θ ) = sen ϕ cos θ + cos ϕ sen θ cos ϕ cos θ cos ϕ cos θ − sen ϕ sen θ cos
ingurunean lehenengoarekiko duen errefrakzio-indize erlatiboa deritzo. s i n θ 1 s i n θ 2 = v 1 v 2 = n 12 {\displaystyle {\frac {sin\theta _{1}}{sin\theta _{2}}}={\frac