I Degrees of freedom and constraints

AI Thread Summary
In systems with P holonomic constraints and N particles, there are 3N-P degrees of freedom, requiring 3N-P generalized coordinates for independent variation. For non-holonomic constraints, despite needing 3N coordinates to fully describe the system, these coordinates do not vary independently due to the constraints imposed. Non-holonomic constraints necessitate more coordinates than degrees of freedom, as they must adhere to specific relationships. The handling of non-holonomic constraints remains an active area of research, with ongoing developments in the field. For further insights, references such as "Flannery nonholonomic" can provide additional information.
Ahmed1029
Messages
109
Reaction score
40
In case of P holonomic constraints and N particles, I have 3N-P degrees of freedom and I have to look for 3N-P generalized coordinates if I want them to vary independently, but what about non-holonomic constraints? I know if I have N particles and P non-holonomic constraints, I still need 3N coordinates to completely describe the mechanical system, but do those 3N coordinates vary independently?(assume I'm talking about any set of coordinates, not just cartesian)
 
Physics news on Phys.org
In systems with non-holonomic constraints, we always need more coordinates than degrees of freedom. Of course, those coordinates do not vary independently, they have to obey the non-holonomic constraint.
 
Reply
  • Like
Likes vanhees71 and Ahmed1029
FYI: the handling of non-holonomic constraints is still an active research area. Google for "Flannery nonholonomic" to see some relevant references.
 
Reply
  • Informative
  • Like
Likes vanhees71, andresB and Ahmed1029

Thread 'Average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
View full post »

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
View full post »

Similar threads

I Constraints of a mechanical system
Replies
5
Views
2K
I Understanding Holonomic Constraints: Common Questions and Answers
Replies
2
Views
1K
I Virtual work and constraint forces
Replies
1
Views
1K
I Independent coordinates are dependent
Replies
9
Views
2K
Understanding Holonomic Constraints in Lagrangian Mechanics
Replies
1
Views
2K
I Can I always consider velocities and coordinates to be independent?
Replies
4
Views
1K
Why do we need the Lagrangian formulation of Mechanics?
Replies
8
Views
2K
Degrees of freedom and holonomic constraints
Replies
15
Views
2K
I Virtual displacement is not consistent with constraints
Replies
3
Views
2K
Configuration Space In Classical Mechanics: Definition
Replies
2
Views
7K

Hot Threads

Recent Insights

Back
Top