Classical Mechanics-System of Particles (IFS Physics (Mains)): Questions 1 - 4 of 4

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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,

Equation

Equation

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

Explanation

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

Equation

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

Equation

  • Equation (2), gives an infinitesimal virtual displacement Equation at particular instant Equation. We can see that the variation with respect to time is absent in equation… (108 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 Equation 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 Equation generalized coordinates Equation. 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 constraints on the system. This kind of displacement is called virtual.

  • In virtual… (231 more words) …

Question number: 4

» Classical Mechanics » System of Particles » Constraints

Appeared in Year: 2010

Essay Question▾

Describe in Detail

How can one introduce the constraints of motion through the concept of generalized coordinate systems? Write down the set of transformation equations for a system of Equation particles relating the generalized coordinates with real coordinates. (Section A)

Explanation

  • In mechanics, mostly problems can be reduced by solving differential equation, which consist of all the forces acting on a system. A such equation is given by,

    Equation

  • As we know, all mechanical systems have constraint force acting on them to some degree. A constrain in which the equations connecting… (208 more words) …

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