## 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 …

## 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 …

## 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 – Sean 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 – Mike Matas: …