Classical Mechanics-System of Particles (IFS Physics): Questions 1 - 3 of 3

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Question number: 1

» Classical Mechanics » System of Particles » Generalised Coordinates and Momenta

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Using D’ Alembert’s principle, show that the following relation can be obtained for a system of particles under generalized coordinates,

iFiδrj=jQjδqj

With,Qj=iFiriqj

What is the significance of Qj ? (Paper-1) (section – A)

Explanation

  • The mathematical statement of D’ Alembert’s principle is given as,

(Fipi˙)δri=0(Eq.1)

  • Transform D’ Alembert’s principle into expressions containing independent generalized coordinates only.

δri=j… (268 more words) …

Question number: 2

» Classical Mechanics » System of Particles » Cyclic Coordinates

Appeared in Year: 2012

Short Answer Question▾

Write in Short

Express Lagrange’s equation of motion for the cyclic coordinate qj and show that the result leads to the general conservation theorem for the generalized momentum coordinates. (Paper - 1) (Section – A)

Question number: 3

» Classical Mechanics » System of Particles » Generalised Coordinates and Momenta

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Starting with Newton’s second law of motion, establish D’ Alembert’s principle and discuss its significance? (Paper-1) (Section –A)

Explanation

  • Let consider a system described by n generalized coordinates qj(j=1, 2,3,,n). And this system undergoes a certain displacement in configuration space. If for this displacement it does not take any time and it is consistent with the… (416 more words) …

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