Timeline for Equations of motion for a spherical pendulum in a non-inertial reference frame
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2013 at 9:19 | history | bounty ended | Rody Oldenhuis | ||
| Aug 30, 2013 at 9:19 | vote | accept | Rody Oldenhuis | ||
| Aug 26, 2013 at 10:38 | comment | added | Spaderdabomb | Do keep me up to date with your progress though =p. Solving for an equation that is complicated enough (such as yours) where using Newtonian forces is highly unrealistic, but then ALSO have a non-conservative system makes for some of the toughest classical dynamics problems that exist (well...there are definitely tougher ones, but this is getting up there). I remember asking my professor once about solving a system like this, and in short he gave me the answer I'm giving you, but he also said Lagrangians and non-conservative systems can get very difficult to deal with | |
| Aug 26, 2013 at 10:35 | comment | added | Spaderdabomb | Well you form your Lagrangian by the method of individually considering kinetic energy and potential energy right? If I were you, I would put this 'corrective' term in the potential energy when you are forming your Lagrangian. So in other words, I would take care of it BEFORE making your Lagrange equations of motion. That way you're less likely to stick something into the equations that has no place in being there. If you put it in the potential energy with the correct sign, the equations should fall out. | |
| Aug 26, 2013 at 10:17 | comment | added | Rody Oldenhuis | Thank you for your answer! Well, I have a fair amount of experience in dealing with non-inertial frames; I;ve just always done it the Newtonian way, by carefully collecting all the (fictitious) forces and simply adding them to get to the equations of motion -- i.e. the question I linked to. I'm just not sure how to accomplish the same using the Lagrangian formalism, so I'll start reading your PDF. Also, dissipation: so I'll have to use Lagrange's equation, with the sum of all non-conservative generalized forces on the RHS and an extra "corrective term" (the dissipation function) on the LHS? | |
| Aug 25, 2013 at 11:46 | comment | added | Edward Hughes | @namehere: indeed the value of the Lagrangian doesn't change (for any given point in phase space). But if you rewrite your coordinates for phase space then the Lagrangian will look different in form. | |
| Aug 25, 2013 at 11:43 | comment | added | resgh | @EdwardHughes Is the difference only in the form of the expression when the Langrangian is expressed in different coordinate systems, and is the value of the Langrangian the same? | |
| Aug 25, 2013 at 10:13 | comment | added | Edward Hughes | The Lagrangian will look superficially different in different coordinates systems, despite being a 'scalar' with respect to some transformations (symmetries). | |
| Aug 25, 2013 at 3:08 | comment | added | resgh | EDIT: I shouldn't have said constant, I mean same. | |
| Aug 24, 2013 at 13:18 | comment | added | resgh | Isn't the Langrangian a scalar? So shouldn't it be constant in all reference frames? | |
| Aug 23, 2013 at 14:07 | history | answered | Spaderdabomb | CC BY-SA 3.0 |