Theoretical MechanicsTopic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion>Generate equations for (x,y), (Vx,Vy), V², T> L = T-U ---For study purposes. Thank you! 7-8. Consider a region of space divided by a plane. The potential energy of a particle inregion 1 is U₁ and in region 2 it is U₂. If a particle of mass m and with speed v₁ in re-gion 1 passes from region 1 to region 2 such that its path in region 1 makes anangle, with the normal to the plane of separation and an angle 02 with the normalwhen in region 2, show thatsin 0₁where T₁ =sin 0₂- (₁=U₁ U₂1/2T₁1 + := mv. What is the optical analog of this problem?

Given that a region of space divided by a plane. The potential energy of a particle in region 1 is…

Answered: Consider a region of space divided by a…

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