Lagrange Mechanics

For most system, the Lagrange function is $L = T – V$, where T is kinetic energy of the system and V is potential energy of the system. Euler-Lagrange Equation for $L(t,q_1 , … , q_n , \dot{q_1}, … , \dot{q_n})$ is: $$\frac{\partial L}{\partial q_i} = \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q_i}} \right), \, i = 1, … , n$$ In …

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Homogeneous Differential Equation

A first order equation $ \frac{dy}{dx} = f(x,y) $ is said to be a homogenous equation if $ f(x,y) = f(tx,ty) $. Steps to solve: Substitute $ y = vx $ into f(x,y) to get $ \frac{dy}{dx} = f(x,vx) $ Differentiate $ y = vx$ to get $ \frac{dy}{dx} = x\frac{dv}{dx} + v $ Substitute the equation you got in …

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Interesting TED Talks

I will be placing TED talks that I find interesting in this post. Enjoy! NOTE: Sorry for the sizing of the videos. I’ll fix it soon. List: Astronomy –┬áSean Carroll: Distant time and the hint of a multiverse – Janna Levin: The sound the universe makes – Carter Emmart demos a 3D atlas of the universe Consumer Electronics –┬áMike Matas: …

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