A particle of mass m is attached to a fixed point 'O' bya weightless inextensible string of length a. It is rouating under the gravity as shown in the figure. The Lagrangian of the particle is is L(0.0) -ma (u* + sin² ug²)- mga cos u where ) and o are the polar angles. The Hamiltonian ofthe particle is:
A particle of mass m is attached to a fixed point 'O' bya weightless inextensible string of length a. It is rouating under the gravity as shown in the figure. The Lagrangian of the particle is is L(0.0) -ma (u* + sin² ug²)- mga cos u where ) and o are the polar angles. The Hamiltonian ofthe particle is:
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Transcribed Image Text:A particle of mass m is attached to a fixed point 'O' bya weightless inextensible string of
length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the
particle is is
83.
L(0,0) =-ma (v + sin? uo?)- mga cose
where 0 and o are the polar angles. The Hamiltonian ofthe particle is:
(a) H=
2ma?
På +
sin 0
-mga cos 0
47
H =.
På
2ma?
sin-e
(b)
+ mga cos 0
(c) H=
(På + Pi)- mga cos0
2ma
(d) H =
P6 + p+ mga cose
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