Timeline for Constraint Equations of a Sphere Rolling Inside another Sphere [closed]
Current License: CC BY-SA 3.0
17 events
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| Jan 18, 2017 at 16:19 | review | Reopen votes | |||
| Jan 18, 2017 at 16:37 | |||||
| Jan 18, 2017 at 16:02 | history | edited | Hosein Rahnama | CC BY-SA 3.0 |
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| Jan 18, 2017 at 12:54 | history | closed |
AccidentalFourierTransform CR Drost John Rennie Kyle Kanos auden |
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| Jan 17, 2017 at 21:47 | answer | added | John Alexiou | timeline score: 1 | |
| Jan 17, 2017 at 20:49 | history | edited | Hosein Rahnama | CC BY-SA 3.0 |
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| Jan 17, 2017 at 20:38 | comment | added | Hosein Rahnama | @jphollowed: Yes. In fact you need to determine the position of one point of the rigid body and then give the proper orientations. In this problem, that point is the center of the sphere whose position is given by $\alpha$ and $\beta$. The orientation should be described using Euler angels. | |
| Jan 17, 2017 at 20:36 | history | edited | Hosein Rahnama | CC BY-SA 3.0 |
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| Jan 17, 2017 at 20:36 | comment | added | user97626 | Why? For three spatial and three angular positions? | |
| Jan 17, 2017 at 20:34 | comment | added | Hosein Rahnama | @jphollowed: A rigid body in general 3D motion have six degrees of freedom! :) $\alpha$ and $\beta$ are general functions of time. :) | |
| Jan 17, 2017 at 20:32 | comment | added | user97626 | but you have one body, giving three spatial coordinates, and two desired constraint equations, right? Doesn't that give one generalized coordinate? Unless you're saying this is a six dimensional problem because the larger sphere is allowed to move. Either way, the angle $\alpha$ should have no time dependence, right? | |
| Jan 17, 2017 at 20:28 | review | Close votes | |||
| Jan 18, 2017 at 12:54 | |||||
| Jan 17, 2017 at 20:24 | history | edited | Hosein Rahnama | CC BY-SA 3.0 |
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| Jan 17, 2017 at 20:19 | comment | added | Hosein Rahnama | @jphollowed: Thanks. :) I just want to derive the constraint equations mathematically. It should be followed from the fact that the velocity of the contact point vanishes. This is a 3D problem so I think one coordinate is not enough. :) | |
| Jan 17, 2017 at 20:17 | history | edited | Hosein Rahnama | CC BY-SA 3.0 |
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| Jan 17, 2017 at 20:15 | comment | added | user97626 | If the ball does not slip, then the system should be describable with just one coordinate - the angle $\beta$, right? Which means you must have two constraints. One of those constraints simply has to do with the fact that the ball does not slip. The other has to do with the fact that the ball will always stay on a unique geodesic, given idealized initial conditions. BTW very nice figure | |
| Jan 17, 2017 at 20:09 | history | edited | AccidentalFourierTransform |
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| Jan 17, 2017 at 20:05 | history | asked | Hosein Rahnama | CC BY-SA 3.0 |