Here I list the undergraduate research program on classical mechanics. The topics are organized mainly in two directions: some of them deal with Lagrangian mechanics (or Hamiltonian) with higher derivative, while others are concerned with integrals of motion.

Project: Noether theorems and higher derivatives

• Literature:
  • Main article: Noether theorems and higher derivatives Paul K. Townsend, arXiv:1605.07128 
  • Higher Order Lagrangians, BSc thesis, Floris Harmanni (pdf)
  • Noether’s theorem in generalized mechanics, D.Anderson, https://iopscience.iop.org/article/10.1088/0305-4470/6/3/005/pdf
• Students: Ege Coban, Dilara Kosva
• Coordinators: Deniz Bozkurt
• Tasks:
• Report: 03.04.2020 (pdf)

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Project: The odd-order Pais–Uhlenbeck oscillator

• Literature:
  • Main article: The odd-order Pais-Uhlenbeck oscillator Ivan Masterov, arXiv:1603.07727
  • The Theorem of Ostrogradsky R. P. Woodard, arXiv:1506.02210
• Students: Ege Aktener, Mehmet Batu Bayindirli, Esra Simsek
• Coordinators: Mustafa Mullahasanoglu
• Tasks:
• Report: 16.04.2020

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Project: Curl Force

• Literature:
  • Main article: Hamiltonian curl forces, Berry and Shukla https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0002
  • Curl force dynamics: symmetries, chaos and constants of motion, Berry and Shukla, https://iopscience.iop.org/article/10.1088/1367-2630/18/6/063018
  • Classical dynamics with curl forces, and motion driven by time-dependent flux, Berry and Shukla, https://iopscience.iop.org/article/10.1088/1751-8113/45/30/305201
• Students: Ersagun Güden, Oğuz Öner
• Coordinators: Ege Eren
• Tasks:
• Report:

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Project: Hamiltonian analysis of second order degenerate Lagrangians

• Literature:
  • Main article: Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians, F. Çağatay Uçgun, O. Esen, H. Gümral, https://arxiv.org/pdf/1701.08494.pdf
• Students: Mert Akdenizli, Mehmet Dede, Ali Pazarcı
• Coordinators:
• Tasks:
• Report: 15.04.2020

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Project: Variational symmetries of Lagrangians

• Literature:
  • Main article: Variational symmetries of Lagrangians, G.F. Torres del Castillo, C. Andrade Miron, and R.I. Bravo Rojas, http://www.scielo.org.mx/pdf/rmfe/v59n2/v59n2a7.pdf
  • Point symmetries of the Euler-Lagrange equations, https://iopscience.iop.org/article/10.1088/1361-6404/aa5563/pdf
  • Variational symmetries as the existence of ignorable coordinates, https://rmf.smf.mx/ojs/rmf/article/view/4064
• Students: Şebnem Karaçubuk, Yüksel Ratib, Nuri Taş
• Coordinators:
• Tasks:
• Report: