{"type":"rich","version":"1.0","title":"Linearisation of the pendulum about its two equilibria","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"\\theta\\approx 0:\\ \\ \\frac{d^{2}\\theta}{dt^{2}}+\\frac{g}{L}\\theta=0;\\qquad \\phi=\\theta-\\pi\\approx 0:\\ \\ \\frac{d^{2}\\phi}{dt^{2}}-\\frac{g}{L}\\phi=0\">\\theta\\approx 0:\\ \\ \\frac{d^{2}\\theta}{dt^{2}}+\\frac{g}{L}\\theta=0;\\qquad \\phi=\\theta-\\pi\\approx 0:\\ \\ \\frac{d^{2}\\phi}{dt^{2}}-\\frac{g}{L}\\phi=0</span>","width":640,"height":320}