Question
Far-field approximations in multipole expansions allow for sub-quadratic complexity in this system, such as in the Barnes–Hut treecode algorithm. Small perturbations in this system lead to large changes in motion in the first-studied “small denominators” problem, which in simulations can be adjusted by applying a “softening parameter” to the potential. The Jacobi integral is an invariant for a form of this system that is “restricted,” which produces five equilibrium points named for Lagrange. In the simplest form of this system, one can fix a reference frame about the center of mass and use the reduced mass, allowing one to derive Kepler’s three laws for a form of this system. For 10 points, name this system concerning the orbits of objects in gravitational central force problems. ■END■
Summary
Great Lakes | 2025-02-01 | Y | 6 | 100% | 0% | 17% | 89.67 |
Lower Mid-Atlantic | 2025-02-01 | Y | 1 | 0% | 0% | 100% | 0.00 |
Midwest | 2025-02-01 | Y | 1 | 100% | 0% | 0% | 100.00 |
Northeast | 2025-02-01 | Y | 3 | 100% | 0% | 0% | 67.67 |
Overflow | 2025-02-01 | Y | 4 | 75% | 0% | 0% | 67.33 |
Pacific Northwest | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 75.50 |
South Central | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 87.50 |
UK | 2025-02-01 | Y | 1 | 100% | 0% | 0% | 64.00 |
Buzzes
Player | Team | Opponent | Buzz Position | Value |
---|---|---|---|---|
Nathan Sheffield | MIT A | Brandeis B | 52 | 10 |
Stan Melkumian | Purdue | Northwestern A | 55 | 10 |
Aditya Patnaik | Ohio State B | Carnegie Mellon B | 64 | 10 |
Agnijo Banerjee | Cambridge A | Oxford A | 64 | 10 |
Joy An | Harvard A | Brown A | 72 | 10 |
Michał Gerasimiuk | Stanford B | Iowa | 72 | 10 |
Catherine Welch | UW A | UW B | 72 | 10 |
Karan Gurazada | Texas A | Texas B | 72 | 10 |
Stephen Heritage | Notre Dame A | Georgetown A | 75 | 10 |
Angelo Pan | Case Western B | Michigan B | 79 | -5 |
Andrew Harms | Michigan State | Case Western A | 79 | 10 |
Isaac Meredith | Tufts A | Brandeis A | 79 | 10 |
Matthew Wang | UBC | Alberta | 79 | 10 |
David Nieman | Carnegie Mellon A | Michigan C | 90 | 10 |
Yashwanth Bajji | Michigan A | Kenyon | 90 | 10 |
Calvin Bostleman | Ohio State A | Michigan D | 90 | 10 |
Ezra Santos | Chicago B | Missouri | 100 | 10 |
Bryan Ugaz | ASU | TAMU | 103 | 10 |
Noah Chin | Virginia Tech A | Virginia A | 105 | -5 |
Mitchell Indek | Michigan B | Case Western B | 125 | 10 |
Joseph Chambers | Virginia A | Virginia Tech A | 125 | 0 |
Christopher Joseph | Notre Dame C | Georgetown B | 125 | 0 |
Amanda Zhao | Georgetown B | Notre Dame C | 125 | 0 |