How does Lagrange Mechanics work in coordinate space?

[Quarlep]

I want to know lagrange mechanics work in phase space or in coordinate system.Leonard Susskind talked about the least action and he said If we know two point we can define trajectory but I don't know the diagram that he drow its a phase space or coordinate system (x,y,z,t)
19 min or something else

thanks

 

[ShayanJ]

That's the coordinate space.