Timeline for Degrees of freedom in restricted circular coplanar three body problem
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2021 at 15:21 | comment | added | Deschele Schilder | Just as a particle moving on a straight line executes just one of its degrees of freedom so are the masses in the plane. You can use any two coordinates to desribe their motion. xy xz yz. Anyhow, it's time to move on. Im done. | |
| Jun 25, 2021 at 11:50 | comment | added | Deschele Schilder | @DavidHammen A mass falling straight to earth falls in one directio. But depending on where you lett the mass fall it has three independent possibilities to fall. So three degrees of freedom. | |
| Jun 25, 2021 at 11:43 | comment | added | David Hammen | @DescheleSchilder From the perspective of a Newtonian inertial frame, there is but one degree of freedom in the Newtonian two body problem. Kepler deduced this without explaining why. Newton later explained why this was the case. In the CR3BP, that singular degree of freedom can easily be eliminated. | |
| Jun 25, 2021 at 11:14 | comment | added | Deschele Schilder | @DavidHammen If the motion is in a mathematical 2d plane (without a third one) then its obvious that there are two degrees for each mass and not zero for two and two for one as is stated in the first answer. The two circing heavy points still have two degrees of freedom. How else can they move on a circle around each other? The problem might be well documented but that doesnt take away the fact that its not physical. | |
| Jun 25, 2021 at 11:07 | comment | added | David Hammen | @DescheleSchilder The Circular Restricted Three Body Problem (CR3BP for short) is a mathematical exercise. You can google "CR3BP" and find lots and lots of articles about this concept. In this problem, the objects are point masses, so there are no rotational degrees of freedom. The two larger masses are frozen in the synodic frame. This is the frame in which the five Lagrange points (aka Lagrangian points, aka libration points) appear. While this is a mathematical simplification, those Lagrange points are real, even in the Elliptical Restricted Three Body Problem (ER3BP for short). | |
| Jun 25, 2021 at 8:51 | comment | added | Deschele Schilder | On top of that the bodies have a rotational degree of freedom too(the real ones). You can make it a math problem but this is an astronomy site. If there were people living on the bodies they would be very disappointed to find they couldnt move in space! I guess its reoutation that talks here (and highly sophisticated use of language covering up the obvious). | |
| Jun 25, 2021 at 8:45 | comment | added | Deschele Schilder | @DavidHammen Im not saying its not correct. It depends. The small mass can move in every direction. Tthis means it has three degrees. The sma holds for the other two masses. What prevents them from moving in other directions? | |
| Jun 25, 2021 at 5:15 | vote | accept | Augustin | ||
| Jun 25, 2021 at 2:19 | comment | added | David Hammen | In other words, this answer is correct. | |
| Jun 25, 2021 at 2:19 | comment | added | David Hammen | @DescheleSchilder The circular restricted three body problem is math. It is always solved in the synodic frame, a non-inertial reference frame that rotates with the orbit of the two larger masses about one another such that neither of the two larger masses is moving in that frame of reference. No motion = zero degrees of freedom. The test mass is an object with negligible mass; it does not perturb the larger masses orbits. The test body is the only body with has any degrees of freedom. With motion constrained to the larger bodies' orbital plane, there are only two degrees of freedom. | |
| Jun 24, 2021 at 21:17 | comment | added | Deschele Schilder | But we are not discussing math here. | |
| Jun 24, 2021 at 21:13 | comment | added | Peter Erwin | Please re-read my answer: I said the restricted problem eliminated the degrees of freedom for the two massive objects; the planar restrictions means there are two degrees of freedom ($x$ and $y$) for the third object. And you are confusing a mathematical problem with reality. | |
| Jun 24, 2021 at 21:06 | comment | added | Deschele Schilder | No degrees of freedom? That makes it pretty hard to move for one mass. You are making the mistake to confuse a state of motion with a boundary induced, material induced restriction of the degrees of freedom. There is no such boundary in this problem so all masses simply have three degrees of freedom. | |
| Jun 24, 2021 at 20:09 | history | answered | Peter Erwin | CC BY-SA 4.0 |