Study Lagrangian Mechanics: D'Alembert's Principle

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SUMMARY

This discussion focuses on Lagrangian mechanics, specifically D'Alembert's principle and the concept of virtual displacement. Virtual displacement is defined as a change in the configuration of a physical system that does not involve a change in time, which distinguishes it from real displacement. The discussion emphasizes the advantages of using D'Alembert's principle over Newtonian mechanics, particularly in simplifying the equations of motion by accounting for constraints. Participants express gratitude for clarifications on these concepts, indicating their complexity and the need for deeper understanding.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with D'Alembert's principle
  • Knowledge of virtual displacement concepts
  • Basic principles of classical mechanics
NEXT STEPS
  • Study the derivation and applications of D'Alembert's principle
  • Explore the differences between Lagrangian and Newtonian mechanics
  • Investigate examples of virtual displacement in constrained systems
  • Learn about the formulation of equations of motion using Lagrangian methods
USEFUL FOR

Students and professionals in physics, particularly those studying classical mechanics, as well as educators seeking to deepen their understanding of Lagrangian mechanics and its applications.

KT KIM
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Studying Lagrangian mechanics starting from D'Alembert's principle.
I just ran into this.
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Why virtual displacement doesn't contain time t for it's coordinates
What does that mean 'take place at a fixed time'?
 
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KT KIM said:
Why virtual displacement doesn't contain time t for it's coordinates

The simplest answer is that its not 'real' displacement therefore it must not contain change in time - and that's why its called 'virtual'

if a geometrical change in the configuration of the physical system is done consistent with the constraints operating on the system then one can formulate a principle which helps in weaning away the force of constrains from equation of motion. and that has certain advantage over Newtonian description.
 
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Thank you much for fine answer, helped me a lot. Guess need some time to grasp that notion well.
 

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