Mathematical Tripos Dynamics and Relativity 2019

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Listed below are my answers to the MT Dynamics and Relativity questions in Paper 4 of Part 1A held in June 2019. Answers to MT D&R questions will be added each October to correspond to the start of Michaelmas Term.

  1. Question 3A. uln2
  2. Question 4A. t = √ (m/(ɣg) ) e-2ɣh/m tanh-1( √(1-e-2ɣh/m) )
  3. Question 9A. A=-1/4, B=3/4
  4. Question 10A. (a) x = 1-r+rcos(⍵t), y = rsin(⍵t), z = vt, where r = mv/( qB √ (1-2v2/c2 ) ) and ⍵=v/r.
  5. Question 10A. (b) (i) (0,0), three saddle points also exist where the equilibrium is stable in one direction (ii) stable along x and y axes. At (0,0) ∂V/∂x=0, ∂V/∂y=0, ∂2V/∂x2>0, ∂V/∂y=0,∂2V/∂y2>0 (iii) A=35/4/(23/2√𝜋). At saddle point ⍵=1.389q/√(m𝜀) taking a=1