Classical Mechanics-System of Particles [IFS (Forest Services) Physics]: Questions 1 - 5 of 26

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Question 1

Appeared in Year: 2012

Describe in Detail Subjective▾

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

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

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Explanation

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

  • Transform D՚Alembert՚s principle into expressions containing inde…

… (107 more equations) …

Question 2

Appeared in Year: 2012

Write in Short Short Answer▾

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

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Question 3

Appeared in Year: 2012

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

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Explanation

  • Let consider a system described by generalized coordinates . And this system undergoes a certain displacement in configuration space. If for this displacement it does not take any time and …

… (122 more equations) …

Question 4

Appeared in Year: 2010

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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 particles relating the generalized coordinates with real coordinates. (Section A)

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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,

… (81 more equations) …

Question 5

Appeared in Year: 2005 (IAS)

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What are constrains of motion, explain with example the holonomic and non-holonomic constraints. Discuss with how one can overcome the limits of constraints by introducing generalised coordinates.

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Explanation

Constraints: often the motion of a particle or system of particles is restricted by one or more conditions. The limitations on the motion of a system are called constraints and the motion is said to be constrained motion.

Holonomic Constraints: constraints limit the motion of a system the number of independent coordination, needed to describe the mo…

… (784 more equations, 21 figures) …