Deriving a mathematical model for a stick falling over

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Discussion Overview

The discussion focuses on deriving a mathematical model for a stick falling over, specifically exploring a simplified model without friction. Participants are examining the relationship between angular motion and vertical motion, and how to eliminate certain accelerations from the model.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant is attempting to create a simple model of a falling stick that incorporates mass, gravitational acceleration, length, angular acceleration, and velocity, while eliminating y-direction acceleration.
  • Another participant suggests that the rotation and motion in the y direction are interdependent and that specifying a constraint could allow for the elimination of one of them.
  • A question is raised about what specific constraint could be used to eliminate the y-direction acceleration, indicating a need for further clarification on the relationship between y and the angle θ.

Areas of Agreement / Disagreement

Participants appear to agree on the interdependence of rotational and vertical motion, but there is no consensus on the specific constraints needed to simplify the model.

Contextual Notes

The discussion does not specify the assumptions underlying the proposed models or the definitions of terms used, which may affect the clarity of the arguments presented.

janneman
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TL;DR
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?
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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.
 
what constraint would let me elimate the acceleration in the y?
 
janneman said:
what constraint would let me elimate the acceleration in the y?
The dependence of ##y## as a function of ##\theta##.
 

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