This website (Mini Physics) offers O and A Level physics revision notes for you to learn Physics online. O Level is equivalent to American High School Diploma and A Level is equivalent to Advanced Placement. If you spot any mistakes in my explanation, please contact the site administrator at Contact Us with the relevant web address and explanation. If you feel …

## 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: …