Equations of motion of a system with non holonomic constraints

[DannyJ108]

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.

 

[wrobel]

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 $q_3,q_4$

 

[DannyJ108]

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.

 

[wrobel]

Also, I didn't mention it, but it says that and are constants independent of the generalized coordinates

you have said this:

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