Semi-holonomic constraints (analytical mechanics)

Click For Summary
SUMMARY

Semi-holonomic constraints in analytical mechanics can be expressed in the form fi=(q1,q2,...,qn,\dot{q}1,...,\dot{qn}). A common representation is given by the equation Σaikdqk + aitdt = 0, where aik and ait are coefficients that may depend on the generalized coordinates q and their derivatives \dot{q}. The discussion clarifies that while the two forms of the equations are not equivalent, the second form represents a frequently encountered special case. Understanding these constraints is crucial for analyzing systems in mechanics.

PREREQUISITES
  • Understanding of generalized coordinates in analytical mechanics
  • Familiarity with differential equations and their applications
  • Knowledge of non-holonomic constraints and their implications
  • Basic proficiency in LaTeX for equation representation
NEXT STEPS
  • Study the derivation and applications of semi-holonomic constraints in analytical mechanics
  • Explore the differences between holonomic and non-holonomic constraints
  • Learn how to represent complex equations using LaTeX
  • Investigate the role of coefficients in constraint equations and their dependence on variables
USEFUL FOR

Students and professionals in physics and engineering, particularly those focusing on analytical mechanics and constraint systems.

maria clara
Messages
56
Reaction score
0
m equations of semi-holonomic constraints can be put in the form:

fi=(q1,q2,...,qn,\dot{q}1,...,\dot{qn})

but "commonly appears in the restricted form:

\Sigmaaikdqk +aitdt = 0

(i,k,t preceded by "a" should appear in subscript and the sum is over k)

I don't understand this form. what are the coefficients aik and ait? can they be functions of q or q dot?
I don't understand how is it possible for these two equations to be equivalent.
consider for example the following equation of a non-holonomic constraint: q1^2+q2dot=0
what would the second form of this equation look like? :confused:
 
Last edited:
Physics news on Phys.org
sorry for the last post (couldn't delete it for some reason)... I was confused, but now I realize the second equation is not exactly equivalent to the first, but represents only a special case which is quite common.
 
maria clara said:
sorry for the last post (couldn't delete it for some reason)... I was confused, but now I realize the second equation is not exactly equivalent to the first, but represents only a special case which is quite common.

I don't think you can delete the first post in a new thread.

Also, have you taken a look at the Latex tutorial? It's an easy way to display equations.
 
now I have, thanks:smile:
 

Similar threads

Graduate Why is Hamilton's Principle assumed to be valid for non-holonomic systems?
  • · Replies 25 ·
Replies
25
Views
3K
Graduate Virtual work of constraint forces in Hamilton’s principle
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Virtual displacement is not consistent with constraints
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Understanding Holonomic Constraints in Lagrangian Mechanics
  • · Replies 1 ·
Replies
1
Views
2K
Does a Particle Moving on a Curve Separate Under Gravity?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Extending Hamilton's principle to systems with constraints
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Analytical Mechanics: Regularity Conditions on Constraint Surface
  • · Replies 7 ·
Replies
7
Views
2K
Particle constrained to move on a hemisphere
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Question on analytic mechanics
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Constraint Forces and Lagrange Multipliers
  • · Replies 1 ·
Replies
1
Views
1K