Vertical circular motion with a changing radius

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SUMMARY

The discussion centers on the mathematical analysis of vertical circular motion involving a stretchable rope, emphasizing the use of Lagrangian mechanics. The rope's constant, denoted as 'k', plays a crucial role in understanding the system's dynamics. Participants highlight the implications of gravity on circular motion and the importance of mass distribution along the rope. This analysis is essential for accurately modeling the behavior of the system under varying conditions.

PREREQUISITES
  • Lagrangian mechanics
  • Understanding of vertical circular motion
  • Concept of elasticity in materials
  • Basic principles of gravity and mass distribution
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  • Explore Lagrangian mechanics in detail
  • Research the effects of elasticity on dynamic systems
  • Study gravitational effects on circular motion
  • Investigate mass distribution models for flexible materials
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Physicists, engineers, and students interested in advanced mechanics, particularly those studying systems involving elasticity and gravitational effects in motion.

ddddd28
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Hello,
I am curious to see how the mathematical analysis of a vertical circular motion with a sensible rope, that is to say, a rope that streches easily, looks like. k- constant of the rope.
thanks,
 
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What have you done so far to get an idea? My tip: Use a Lagrangian!
 
stretchable rope is of infinitely many degrees of freedom system even though the rope lies on a straight fixed line.

In addition to this OP says "vertical motion" this implies gravity. Then what is a circular motion in this context?
And how is mass distributed along the rope?
 
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