Deriving a mathematical model for a stick falling over

[janneman]

TL;DR Summary

build a mathematical model that describes the motion of a stick falling over

this is how far i have come with my model, i am trying to first the most simple model, meaning no friction involved and then testing that against an actual stick falling by using tracking software. I am currently stuck as my model still has an acceleration in the y direction that i cannot seem to get rid off. i am trying to model it only in terms of mass gravitational acceleration length and the angular acceleration and velocity. Could one use relative motion analyses to get rid of the acceleration in the y?

 

[PeroK]

The rotation and the motion in the y direction are dependent on each other. If you can specify the constraint, then you can eliminate one of them.

 

[janneman]

what constraint would let me elimate the acceleration in the y?

 

[PeroK]

what constraint would let me elimate the acceleration in the y?

The dependence of $y$ as a function of $\theta$.