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Look at the one dimensional motion of relativistic particle of paper number (look at the bottom) a) Calculate the Hamiltonian- Function of the system and b) derive of this the Hamiltonian equation of motion Please do not calculate number again. wrote the solution next to them. 3 The one motion of relativistic particle with the velocity and the mass min the Potential V(x) described by the Lagrange function cisthe speed of light, 7= 1 the Lorentz factor and p= ymv the kinetic momentum (a) get the Equations of motion se (b) To which function converges the lagrangian function the non relativistic case. if only term till the O-order v/c are considered? (c) Which Langrange function do youget, fonly terms till the order 1 2 (2² are considered? Wants the associated Equations of motion. =mv'+3/2 m v^2 (v /c^2) Look number 4 (look at the bottom). a) Calculate the Function of the system and b) derive of this the Hamiltonian equation of motion Please do again. wrote the solutions next to them wheel The cord/fiber has no mass Ablock side. attached has the mass The the side (look put It is like thin disk thickness anda mass density p(r) 2Mr² to the centre f mass cord works like belt (mechanical). It means: he does not glide around the wheel. a) Calculate the b) Show that the disk only c) Find plays d) Give where e) f)Solve out of equilibriumbb the olute value x(0) and Be f f(91,92,P1.P2.1). 11(91,92,P1.P2,1) two times differentiable functions and H the Hamiltonian function of system with two degrees of freedom Show that the following identities for the Poisson bracket a) (f.8)=(8.f) dt at af dq Aparticle with mass moves in the central potential a U(t.x.y.z) v.a>>0. (x-17)2+1242 Therewith y is the velocity of the center of the potential in -direction. a) Give the Hamiltonian function p.t) of this system and b) derive of this the Hamiltonian equation of motion c) Show, that the phase space transformation 5 =x-vt. P1 Px is canonical and d) calculate the corresponding generating function F, that depends on t,x and Px e) Show, that the potential in the new coordinates is static (its centrum does not move) f) Calculate the transformed Hamiltonian function A(O.P.1) of this system and g) derive of this the transformed Hamiltonian equation of motion.

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