Semi-holonomic constraints (analytical mechanics)

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Homework Help Overview

The discussion revolves around the topic of semi-holonomic constraints in analytical mechanics, specifically focusing on the forms of equations representing these constraints and their equivalence to non-holonomic constraints.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the meaning of coefficients in the semi-holonomic constraint equation and questions their dependence on generalized coordinates and velocities. They also seek clarification on the equivalence of two forms of constraint equations.

Discussion Status

Some participants acknowledge confusion regarding the relationship between the two forms of equations and clarify that one represents a special case of the other. There is an indication of productive exploration of the topic, with references to additional resources like a LaTeX tutorial for better equation representation.

Contextual Notes

The original poster expresses uncertainty about the equivalence of the equations and the nature of the coefficients involved, indicating a need for further exploration of these concepts within the constraints of the homework context.

maria clara
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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:
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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:
 

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