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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.
I have also branched out into mathematical demography. What fascinates me there is the modeling of various aspects of biodemographic systems and their dynamics, including the relationship between life span and life span inequality, and the dynamics of mortality across time and species.
Below I list (and embed) my research publications. Entries of the form “XXB” indicate books or book chapters; those of the form “XXT” indicate contributions to the scholarship on teaching and learning. Talks and posters based on those publications are listed in my CV and are also available on the Presentations page.
Publication Timeline
Publication Timeline
2025
2025
1 book
26. (Book) Fernandez, O.E. Calculus 2 Simplified. Under contract with Princeton, NJ: Princeton University Press. Expected publication date: Summer 2025.
2023
2023
1 research article
25. Fernandez, O.E. Improved Bounds and High-Accuracy Estimates for Remaining Life Expectancy via Quadrature Rule-Based Methods. Demographic Research, 48(27) (2023), 809-828. [doi]
Fernandez - Dem Res 2023.pdf2022
2022
3 research articles
24. 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. [doi]
rsos.220020.pdf23. Fernandez, O.E. Quantizing Chaplygin Hamiltonizable nonholonomic systems. Scientific Reports, 12 (2022), Article number: 9414. [doi]
s41598-022-13335-6.pdf22. 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. [doi]
journal.pone.0262869.pdf2021
2021
1 SoTL article
21T. 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]
Fernandez 2021.pdf2020
2020
1 SoTL article
20T. 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]
Fernandez - PRIMUS 2020.pdf2019
2019
1 book
19B. (Book) Fernandez, O.E. Calculus Simplified. Princeton, NJ: Princeton University Press (June 2019). Translations published in: Chinese, Korean. [Click here to read the first chapter.]
2018
2018
1 research article
1 book chapter
18. Fernandez, O.E. and Radhakrishnan, M.L. The Quantum Mechanics of a Molecular "Nanocar." Scientific Reports 8, Article Number: 14878 (2018). [open access link]
17B. (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).
Fernandez 2018.pdfFernandez 2018 - Book chapter.pdf2017
2017
1 book
1 book chapter
16B. (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, Korean, Japanese, and Portuguese. [Click here to read the first chapter.]
15B. (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
2015
3 research articles
14. Fernandez, O.E. and Beltrán-Sánchez, H. The Entropy of the Life Table: A Reappraisal. Theor. Pop. Biology, 104 (2015), 26-45. [doi]
13. Balseiro, P. and Fernandez, O.E. Reduction of nonholonomic systems in two stages. Nonlinearity, 28(8) (2015), 2873-2912. [doi]
12. Fernandez, O.E. Poincare Transformations in Nonholonomic Mechanics. Appl. Math. Lett., 43 (2015), 96-100. [doi]
Fernandez 2015-1.pdfFernandez 2015-2.pdfFernandez 2015-3.pdf2014
2014
2 research articles
1 book
11B. (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: Korean, Japanese, and Portuguese. [Click here to read the first chapter.]
10. Fernandez, O.E., Bloch, A.M. and Zenkov, D.V. The Geometry and Integrability of the Suslov Problem. J. Math. Phys., 55 (2014), 112704. [doi]
9. Fernandez, O.E. Quantizing Conditionally Variational Nonholonomic Systems. J. Phys. A: Math. Theor., 47(30) (2014), 305206. [doi]
OEFAMBDVZ2014.pdfOEFJul2014.pdf2012
2012
1 research article
8. Fernandez, O.E., Bloch, A.M. and Olver, P.J. Variational Integrators for Hamiltonizable Nonholonomic Systems. J. Geometric Mechanics, 4(2) (2012), 137-163. [doi]
OEFPJO2012.pdf2011
2011
2 research articles
7. 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. [doi]
6. Fernandez, O.E. and Bloch, A.M. The Weitzenbock Connection and Time Reparameterization in Nonholonomic Mechanics. J. Math. Physics, 52 (2011), 012901. [doi]
NHHJOFBZ11.pdfOEFAMBWeitzen.pdf2009
2009
3 research articles
1 thesis
5. 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. [doi]
4. 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).
3. 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. [doi]
Fernandez, O.E. [Thesis] The Hamiltonization of Nonholonomic Systems and its Applications. University of Michigan, Ann Arbor (2009).
GenChapBFM.pdfBrussels_MBF.pdfHamiltonizationBFM.pdfThesis.pdf2008
2008
2 research articles
2. 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. [doi]
1. 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. [doi]
FBM2008.pdfEquiv08_FB.pdfThesis
Thesis
2009
0. Fernandez, O.E. The Hamiltonization of Nonholonomic Systems and its Applications. Thesis, University of Michigan,
Thesis.pdfPage updated
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