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)
EditExplanation
- 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)
EditQuestion 3
Appeared in Year: 2012
Describe in Detail Subjective▾
Starting with Newton՚s second law of motion, establish D՚Alembert՚s principle and discuss its significance? (Paper-1) (Section – A)
EditExplanation
- 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)
EditExplanation
- 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)
Describe in Detail Subjective▾
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.
EditExplanation
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) …