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Classical Mechanics Mock Papers
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  • Course
  • Classical Physics
  • Institution
  • Classical Physics
  • Book
  • Analytical Mechanics

Compilation of semester exam level questions in Classical Mechanics on following topics. VARIATIONAL CALCULUS - Euler equation, Lagrange multipliers, Holonomic and Non-holonomic constraints. LAGRANGIAN MECHANICS - degrees of freedom, virtual work, generalised coordinates, velocities and forces, c...

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  • May 7, 2023
  • 5
  • 2022/2023
  • Other
  • Unknown

Subjects

  • variational principle
  • lagrangian
  • hamilton
  • euler
  • gauge
  • lorentz
  • normal modes
  • central force
  • orbit
  • canonical transformation
  • jacobi
  • rigid body
  • reference frame
  • rotation
  • centre of mass
  • inertia

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  • Classical Physics
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. Apendnlun with a masslcss string of length ) and mass mis hanging fron aniong
platfor1which has a constant accclcration cí. starting from an initial clocitr (Gt
itational acccloration () acts along -j. The string makcs an anglc ) with thc rertical.

a) Obtain the kinctic cncrgy of this srsten in the ground framc at rest (not the moNing
frame of the platforn) in tems of the gcncralizcd rariablc 0.

b) Use virt ual work to obtain gcncrali cd force F and obtain the cquation of
ms of 0and its timc dorivatives usi.g and Fn.
(3 + 2 =5 marks)
2. Show that Lagrangcs cquation ( ) - =F. where 7 is the kinctic cncrgy and F is
the gencraliscd force. is cquivalcnt to the cquation - 2=F (2.5 mnarks).
3. Ile have lcarnt the invariancc propcrty that the Largrangian cquatiol C Nl.
Luxder the transformation :: L. ’ '= l.+t0) Hore /. = Li9, q, !) where 4s te
gencralizcd variablc and / docs not depcnd on

The Ligrangian of acharge y in magnrtir ficld /: is given hr 7= 7 4
where. is themagnctic vector potcnt ial and o is the scalar potcntial. Explot tie abore
invariance propcrtr. to show that a gange transformation giren br


kecps the Lagrangian cquation invariant.
(Although you will not nced this here, for complcteness sakr. 1: = -D4
(2.5 marks)

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