## Transcribed Text

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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