Equations of motion of a system with non holonomic constraints

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DannyJ108
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Homework Statement
A system with 2 degrees of freedom has 2 non holonomic constraints. Determine the equations of motion that can describe the movement of such system
Relevant Equations
##A_1 dq_1 +Cdq_3 + Ddq_4 = 0##
##A_2 dq_1 + Bdq_2 = 0##
Hello,

I have a system with 2 degrees of freedom with 2 non-holonomic constrains that can be expressed by:##A_1 dq_1 +Cdq_3 + Ddq_4 = 0##

##A_2 dq_1 + Bdq_2 = 0##Being ##q_1, q_2, q_3## and ##q_4## four generalized coordinates that can describe the movement of the system. And ##A_1, A_2, B, C## and ##D## independent constants.I have to obtain the necessary equations to completely describe the system's motion and interpret the physical meaning of the different equations.How should I proceed? I think I should use Lagrange multipliers, but I don't know where to start.Thanks for the help.
 
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If A,B,C,D are constants then the constraints are holonomic. Integrate these equations:
$$ A_1 q_1+Cq_3+Dq_4=const_1,\quad A_2q_1-Bq_2=const_2$$ express from here for example ##q_1,q_2## and get the system with generalized coordinates ##q_3,q_4##
 
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wrobel said:
If A,B,C,D are constants then the constraints are holonomic. Integrate these equations:
$$ A_1 q_1+Cq_3+Dq_4=const_1,\quad A_2q_1-Bq_2=const_2$$ express from here for example ##q_1,q_2## and get the system with generalized coordinates ##q_3,q_4##

The homework statement specifically says that the constants are non holonomic, so approaching them as holonomic would be wrong I think.
Also, I didn't mention it, but it says that ##A_1, A_2, B, C## and ##D## are constants independent of the generalized coordinates. I'm not sure if it makes a difference in the way to resolve the exercise.
I'll try the approach you mentioned.
 
DannyJ108 said:
Also, I didn't mention it, but it says that and are constants independent of the generalized coordinates
you have said this:
DannyJ108 said:
Homework Statement:: A system with 2 degrees of freedom has 2 non holonomic constraints. Determine the equations of motion that can describe the movement of such system
Relevant Equations:: A1dq1+Cdq3+Ddq4=0
A2dq1+Bdq2=0

. And and independent constants.
By the way the rang of constraints matrix must be 2