I Study Lagrangian Mechanics: D'Alembert's Principle

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Virtual displacement in Lagrangian mechanics does not include time because it represents an idealized change in a system's configuration that occurs instantaneously, without real movement. This concept is crucial for understanding D'Alembert's principle, which allows for the separation of constraint forces from the equations of motion. By considering virtual displacements, one can derive equations that simplify the analysis of dynamic systems compared to traditional Newtonian mechanics. The discussion emphasizes the importance of grasping these foundational concepts for a deeper understanding of Lagrangian mechanics. Overall, mastering virtual displacement is essential for effectively applying D'Alembert's principle in mechanics.
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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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