Newtonian mechanics and Hamiltonian mechanics
To find the trajectory of a ball thrown with an initial speed $v_0$ at an angle $\theta$ (projectile motion), we will set up our coordinate system where $x$ is the horizontal distance and $y$ is the vertical height. we consider a particle of mass $m$ in a uniform gravitational field $\mathbf{g} = -g\hat{\mathbf{j}}$. The motion … Read more