Motion described by differential equations

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Homework Help Overview

The discussion revolves around the derivation of two differential equations related to motion, as presented in a classical mechanics textbook. Participants are exploring how these equations are set up based on graphical representations and constraints of the system.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about the derivation of the differential equations and question the assumptions related to constraints on the system, such as motion on a plane and rolling without slipping. Some participants suggest that the equations can be derived from these constraints.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the derivation process and the role of constraints. There is an indication that some guidance has been offered regarding the constraints, but no consensus or resolution has been reached.

Contextual Notes

Participants note that the equations are presented in a textbook without detailed derivation, leading to confusion. There is also a mention of the difficulty in receiving responses due to the format of the posted equations.

diredragon
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Homework Statement


Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up?

Homework Equations

The Attempt at a Solution


I don't have a slightest clue as how are these equations derived in the first place.
 

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diredragon said:

Homework Statement


Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up?

Homework Equations

The Attempt at a Solution


I don't have a slightest clue as how are these equations derived in the first place.

They can be derived from the constraints on the system.

If it's moving on a plane, z is constant.
It's perpendicular to the plane.
It remains perpendicular to the plane.
And we can assume it's rolling without slipping.

You can re-derive everything from those four constraints.
 
So how exactly did they get to those two diff equations? The book just wrote them down. And its the first time I am hearing about constraints, read it a while ago though...
 
diredragon said:

Homework Statement


Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up?

Homework Equations

The Attempt at a Solution


I don't have a slightest clue as how are these equations derived in the first place.

Please type out the equations; posting sideways-oriented photos will not bring you responses from most helpers.
 

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