Motion described by differential equations

[diredragon]

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.

 

[Student100]

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.

 

[diredragon]

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...

 

[Ray Vickson]

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.