Publications
My research interests originate from my fascination with the interplay between mathematics and physics. In particular, I study geometric mechanics, which can most easily be described as mechanics on manifolds.
A particularly interesting related field is that of nonholonomic mechanics. These are mechanical systems subjected to non-integrable constraints on the velocities of the system. Some familiar examples of nonholonomic systems are cars and bowling balls (assuming they roll without slipping). It turns out that these systems are not Hamiltonian. However, under certain conditions they can be embedded in a larger Hamiltonian system. Much of my prior research has focused on finding different ways to do this. Lately I have been exploring the applications of these results to questions like the integrability and quantization of nonholonomic systems.
Below I list my research publications. Talks and posters based on those publications are listed in my CV.
Publication Timeline
2022
Fernandez, O.E. and Beltrán-Sánchez, H. On the Emergence of the Correlation
between Life Expectancy and the Variance in the Age at Death. Royal Society Open Science. 9:220020. 220020. [pdf] [doi]
Fernandez, O.E. Quantizing Chaplygin Hamiltonizable nonholonomic systems. Scientific Reports, 12 (2022), Article number: 9414. [pdf] [doi]
Fernandez, O.E. and Beltrán-Sánchez, H. Life span inequality as a function of the moments of the deaths distribution: connections and insights. PLoS ONE 17(1):e0262869. [pdf] [doi]
2021
Korstange, R., Blum, S.D., Fernandez, O.E. Imad, M., Nelson Laird, T.F., and Pantelides, K.L. A Theory of Public Higher Education. Soundings: An Interdisciplinary Journal, 104(2-3) (2021), 141-251. [doi]
2020
Fernandez, O.E. Second Chance Grading: An Equitable, Meaningful, and Easy-to-Implement Grading System that Synergizes the Research on Testing for Learning, Mastery Grading, and Growth Mindsets. PRIMUS, 31(8) (2020), 855-868. [doi]
2019
(Book) Fernandez, O.E. Calculus Simplified. Princeton, NJ: Princeton University Press (June 2019). Translations published in: Chinese, Korean.
2018
Fernandez, O.E. and Radhakrishnan, M.L. The Quantum Mechanics of a Molecular "Nanocar." Scientific Reports 8, Article Number: 14878 (2018). [open access link]
(Book Chapter) Fernandez, O.E. How Constructivism Can Boost Success in STEM Fields for Women and Students of Color. In D. Kritt (Eds.), Constructivist Education in an Age of Accountability. Cham, Switzerland: Palgrave Macmillan (January 2018).
2017
(Book) Fernandez, O.E. The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love. Princeton, NJ: Princeton University Press (April 2017). Translations published in: Chinese, Japanese, Korean, and Portuguese.
(Book Chapter) Fernandez, O.E. Help Save the Planet: Take the 1/2 CO2e Challenge! In B. Kateman (Eds.), The Reducetarian Solution: How the Surprisingly Simple Act of Cutting 10% of Meat from Your Diet Can Transform Your Health and The Planet. Harmondsworth, UK: Penguin Books (April 2017).
2015
Fernandez, O.E. and Beltrán-Sánchez, H. The Entropy of the Life Table: A Reappraisal. Theor. Pop. Biology, 104 (2015), 26-45. [pdf] [doi]
Balseiro, P. and Fernandez, O.E. Reduction of nonholonomic systems in two stages. Nonlinearity, 28(8) (2015), 2873-2912. [pdf] [doi]
Fernandez, O.E. Poincare Transformations in Nonholonomic Mechanics. Appl. Math. Lett., 43 (2015), 96-100. [pdf] [doi]
2014
Fernandez, O.E., Bloch, A.M. and Zenkov, D.V. The Geometry and Integrability of the Suslov Problem. J. Math. Phys., 55 (2014), 112704. [pdf] [doi]
Fernandez, O.E. Quantizing Conditionally Variational Nonholonomic Systems. J. Phys. A: Math. Theor., 47(30) (2014), 305206. [pdf] [doi]
(Book) Fernandez, O.E. Everyday Calculus: Discovering the Hidden Math All Around You. Princeton, NJ: Princeton University Press (April 2014). Translations have been published in Japanese, Korean, and Portuguese.
2011
Ohsawa, T., Fernandez, O.E., Bloch, A.M. and Zenkov, D.V. Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization. J. Geometry and Physics, 61(8) (2011), 1263-1291. [pdf] [doi]
Fernandez, O.E. and Bloch, A.M. The Weitzenbock Connection and Time Reparameterization in Nonholonomic Mechanics. J. Math. Physics, 52 (2011), 012901. [pdf] [doi]
2009
Fernandez, O.E., Mestdag, T. and Bloch, A.M. A Generalization of Chaplygin's Reducibility Theorem. Reg. and Chaotic Dyn., 14(6) (2009), 635-655. [pdf] [doi]
Mestdag, T., Bloch, A.M. and Fernandez, O.E. Hamiltonization and Geometric Integration of Nonholonomic Systems. Proc., 8th Nat. Congress on Theor. and Appl. Mechanics, Brussels, Belgium (2009). [pdf]
Bloch, A.M., Fernandez, O.E. and Mestdag, T. Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations. Rep. Math. Phy., 63 (2009), 225-249. [pdf] [doi]
2008
Fernandez, O.E., Bloch, A.M. and Mestdag, T. The Pontryagin Maximum Principle applied to Nonholonomic Mechanics. Proc. IEEE 47th Control Decision Conf., (2008), 4306-4311. [pdf] [doi]
Fernandez, O.E. and Bloch, A.M. Equivalence of the Dynamics of Nonholonomic and Variational Nonholonomic Systems for certain Initial Data. J. Phys. A: Math. Theor., 41(34) (2008) 344005. [pdf] [doi]