Research Interests

My primary area of research is celestial mechanics, which seeks to describe the motion of a fixed number of point masses under Newton's laws of motion and gravity. This problem has intrigued mathematicians for centuries, and continues to have an active community of researchers.

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One of the most famous periodic orbits discovered recently is the figure-eight orbit of Moore, Chenciner, and Montgomery, illustrated above. This type of orbit is known as a choreography. A choreography is a periodic orbit in which all the bodies trace out the same curve, with only a time shift separating them.

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Other types of periodic orbits exist. Above is a system of three unequal masses.

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I study periodic orbits that feature collisions between two or more masses, like the one pictured above. After the collision, the bodies rebound in an elastic fashion, similar to billiard balls. Although real-world collisions don't behave this way, studying what happens in the case of collision can help us understand the nearby non-collision orbits.

Pre-publication Works

  1. S., The Eight-Body Cubic Collision-Based Periodic Orbit, submitted.

Published & Accepted Papers

  1. S., Stabilty of Broucke's Isosceles Orbit, Discrete and Continuous Dynamical Systems A, Vol. 41 (2021) No. 8.
  2. Bakker, S., A Separating Surface for Sitnikov-Like n+1-body Problems, Journal of Differential Equations, Vol. 258 (2015) No. 9.
  3. Bakker, S., Stability of the Rhomboidal Symmetric-Mass Orbit, Discrete and Continuous Dynamical Systems A, Vol. 35 (2015) No. 1.
  4. Fisher, S., Topological Properties of Invariant Sets for Two-Dimensional Hyperbolic Toral Automorphisms, Dynamical Systems: An International Journal, Vol. 30 (2015) No. 1.
  5. Bakker, Mancuso, S., Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem, Journal of Mathematical Analysis and Applications, Vol. 392 (2012) No. 2.
  6. Bakker, Ouyang, S., Yan, Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem, Celestial Mechanics and Dynamical Astronomy, Vol. 110 (2011) No. 3.
  7. Bakker, Ouyang, Roberts, S., Yan, Linear Stability for Some Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem, Celestial Mechanics and Dynamical Astronomy, Vol. 108 (2010) No. 2.
  8. Ouyang, S., Yan, Periodic Solutions with Singularities in Two Dimensions in the n-body Problem, Rocky Mountain Journal of Mathematics, Vol. 42 (2012) No. 5.