Firdaus Udwadia: Selected Recent Publications in Science & Engineering    

• Cho, H., and Udwadia, F.E., "Explicit Control Force and Torque Determination for Satellite Formation-Keeping with Attitude Requirements", Journal of Guidance, Control and Dynamics, 2013, DOI: 10.2514/1.55873 PDF 
• Udwadia, F.E., and Cho, H., "Lagrangians for Damped Linear Multi-Degree-of-Freedom Systems", Journal of Applied Mechanics, 1, 441, 2012, DOI:10.1115/1.4023019 PDF 
• Udwadia, F.E., and Schutte, A.D., "A Unified Approach to Rigid Body Rotational Dynamics and Control", Proceedings of the Royal Society of London, Series A, Vol. 468, pp. 395-414, 2012. PDF 
• Udwadia, F.E., Leitmann, G., and Cho, H., "Some Further Remarks on Hamilton's Principle", Journal of Applied Mechanics, Vol. 78, pp. 011014-1 to 011014-4, 2011. PDF 
• Udwadia, F.E., "On the Longitudinal Vibrations of a Bar with Viscous Boundaries: Super-stability, Super-instability, and Loss of Damping", International Journal of Engineering Science, Volume 50, Issue 1, Pages 79-100, January 2012. PDF 
• Schutte, A.D., Udwadia, F.E., "New Approach to the Modeling of Complex Multibody Dynamical Systems", Journal of Applied Mechanics, Vol. 78, pp. 021018-1 to 021018-11, 2011.PDF 
• Udwadia, F.E., Massa, G.D., "Sphere Rolling on a Moving Surface: Application of the Fundamental Equation of Constrained Motion", Simulation Modelling Practice and Theory, Volume 19, Issue 4, Pages 1118-1138, April 2011.PDF 
• Udwadia, F.E., Schutte, A.D, "Equations of Motion for General Constrained Systems in Lagrangian Mechanics", Acta Mechanica, Vol. 213, pp. 111-129, Feb. 2010. PDF 
• Cho, H., Udwadia, F.E., "Explicit Solution to the Full Nonlinear Problem for Satellite Formation-Keeping", Acta Astronautica, Vol. 67, pp. 369-387, 2010. PDF 
• Udwadia, F.E., Schutte, A.D, "An Alternative Derivation of the Quaternion Equations of Motion for Rigid-Body Rotational Dynamics", Journal of Applied Mechanics, Vol. 77, 044505, pp. 1-4, 2010. PDF 
• Udwadia, F.E., and Wanichanon, T., "Hamel's Paradox and the Foundations of Analytical Dynamics", Applied Mathematics and Computations, Vol. 217, pp. 1253-1263, 2010. PDF 
• Waters, M.S., El-Naggar, M.Y., Hsu, L., Sturm, C.A., Luttge, A., Udwadia, F.E., Cvitkovitch, D.G., Goodman, S.D., and Nealson, K.H.,"Simultaneous Interferometric Measurement of Corrosive or Demineralizing Bacteria and Their Mineral Interfaces", Applied and Environmental Microbiology, Vol. 75, No. 5, pp. 1445-1449, March 2009. PDF 
• Waters, M.S., Salas, E.C., Goodman, S.D., Udwadia, F.E., and Nealson, K.H."Early Detection of Oxidized Surfaces using Shewanella Oneidensis MR-1 as a Tool", Biofouling, Vol. 25, No. 2, pp. 163-172, February 2009. PDF 
• Udwadia, F.E., "A Note on Nonproportional Damping", Journal of Engineering Mechanics, Vol. 135, pp. 1248-1256, November 2009. PDF 
• Di Carlo, T., Khoshnevis, B., and Udwadia, F.E., "Whole-Brain Thinking in Systems Architecting", Journal of Systems Engineering, DOI 10.1002/sys.20121, 2008. PDF 
• Udwadia, F.E., Farahani, A., "Accelerated Runge-Kutta Methods", Discrete Dynamics in Nature and Society, Vol. 2008, Article ID 790619, 38 pages, 2008. PDF 
• Udwadia, F.E., "Optimal Tracking Control of Nonlinear Dynamical Systems", Proceedings of the Royal Society of London, Series A, Vol. 464, pp. 2341-2363, 2008. PDF 
• Waters, M.S., Sturm, C.A., El-naggar, M.Y., Luttge, A., Udwadia, F.E., Cvitkovitch, D.G., Goodman, S.D., and Nealson, K.H. "In Search of the Microbe/Mineral Interface: Quantitative Analysis of Bacteria on Metal Surfaces Using Vertical Scanning Interferometry", Geobiology, Vol. 6 , pp. 254-262, 2008. PDF 
• Peters, J., Mistry, M., Udwadia, F.E., Nakanishi, J., Schaal, S., "A Unifying Framework for Robot Control with Redundant DOFs", Autonomous Robots, Vol. 24 , pp. 1-12, 2008. PDF 
• Udwadia, F.E., and Han, B., "Synchronization of Multiple Chaotic Gyroscopes Using the Fundamental Equation of Mechanics", Journal of Applied Mechanics, Vol. 75 ,02011, 2008. PDF 
• Kim, D., Udwadia, F.E., and Proskurowski W., "A Perturbation Approach for Approximate Inertial Manifolds", International Journal of Computational and Applied Mathematics, Vol. 2 (1), pp. 15-41, 2007. PDF 
• Udwadia, F.E., and Phohomsiri, P., "Generalized LM-inverse of a Matrix Augmented by a Column Vector", Applied Mathematics and Computation, Vol. 190 (2007), pp. 999-1006, 2007. PDF 
• Udwadia, F.E., and Phohomsiri, P., "Explicit Poincare Equations of Motion for General Constrained Systems. Part I. Analytical Results," Proceedings of the Royal Society of London, Series A, Vol. 463 (2082), pp. 1421-1434, 2007. PDF 
• Udwadia, F.E., and Phohomsiri P., "Explicit Poincare Equations of Motion for General Constrained Systems. Part II. Applications to Multi-body Dynamics and Nonlinear Control," Proceedings of the Royal Society of London, Series A,Vol. 463 (2082), pp. 1435-1446, 2007. PDF 
• Udwadia, F.E., Hubertus von Bremen, Phohomsiri, P., "Time-delayed Control Design for Active Control of Structures: Principles and Applications," Structural Control and Health Monitoring, Vol. 14 (1), pp. 27-61, 2007. PDF 
• Udwadia, F.E., and Phohomsiri, P., "Explicit Equations of Motion for Constrained Mechanical Systems with Singular Mass Matrices and Applications to Multi-body Dynamics," Proceedings of the Royal Society of London, Series A, 462, pp. 2097-2117, July, 2006. PDF 
• Udwadia, F.E., G. Leitmann, and L. Lambertini, "A Dynamical Model of Terrorism," Discrete Dynamics in Nature and Society, Doi:10.1155/DDNS/2006/85653, pp. 1-32, 2006. PDF 
• Udwadia, F.E., and Phohomsiri, P., "Recursive Formulas for the Generalized LM-Inverse of a Matrix," Journal of Optimization Theory and Applications, Vol. 131 (1) pp. 1-16, October 2006. PDF 
• Udwadia, F.E., "Recent Advances in Multi-body Dynamics and Nonlinear Control," J. of the Braz. Soc. of Mech. Sci. & Eng., Vol. XXVIII  (3) pp. 311-315, July-September 2006. PDF 
• Phohomsiri P., Udwadia, F.E., and H. Von Bremmen, "Time-Delayed Positive Velocity Feedback Control Design for Active Control of Structures," Journal of Engineering Mechanics, Vol. 132 (6) pp. 690-703, June 2006. PDF 
• Udwadia, F.E., and Phohomsiri, P., "Active Control of Structures Using Time Delayed Positive Feedback Proportional Control Designs," Structural Control and Health Monitoring, Vol. 13 (1), pp. 536-552, 2006. PDF 
• Udwadia, F.E., "In Memory of Robert E. Kalaba," Journal of Optimization Theory and Applications, Vol. 127 (3), pp. 471-473, 2005. PDF
• Fan Y. Y.,Kalaba, R. E.,Natsuyama H. H.,and Udwadia, F.E., "Reflections on the Gauss Principle of Least Constraint," Journal of Optimization Theory and Applications, Vol. 127 (3), pp. 475-484, 2005. PDF
• Udwadia, F.E., "Equations of Motion for Constrained Multibody Systems and their Control," Journal of Optimization Theory and Applications, Vol. 127 (3), pp. 627-638, 2005. PDF
• Udwadia, F.E., and Phohomsiri, P., "Recursive Determination of the Generalized Moore-Penrose M-Inverse of a Matrix," Journal of Optimization Theory and Applications, Vol. 127 (3), pp. 639-663, 2005. PDF 
• Udwadia, F.E., "Structural Identification and Damage Detection from Noisy Modal Data," Journal of Aerospace Engineering, Vol. 18 (3), pp. 179-187, 2005. PDF
• Udwadia, F.E., "On Constrained Motion", Applied Mathematics and Computation, Vol. 164, pp. 313-320, 2005. PDF
• Udwadia, F.E., "Boundary Control, Quiet Boundaries, Super-stability and Super-instability," Applied Mathematics and Computation, Vol. 164, pp. 327-349, 2005. PDF
• Udwadia, F.E., "New General Principle of Mechanics and Its Application to General Nonideal Nonholonomic Systems," Journal of Engineering Mechanics, Vol. 131 (4), pp. 444-450, 2005. PDF
• Udwadia, F.E., Kalaba, R.E., Phohomsiri, P., "Mechanical Systems with Nonideal Constraints: Explicit Equations Without the Use of Generalized Inverses," Journal of Applied Mechanics, Vol. 71 (5), pp. 618-621, 2004. PDF
• Phohomsiri, P., Udwadia, F.E., "Acceleration of Runge-Kutta Integration Schemes," Discrete Dynamics in Nature and Society, 2004:2, pp. 307-314, 2004. PDF
• Wiederien, R.J., Udwadia, F.E., "Global Patterns from Local Interactions: A Dynamical Systems Approach," International Journal of Bifurcation and Chaos, Vol. 14, No. 8, pp. 2555-2578, 2004. PDF
• Udwadia, F.E., "A New Perspective on the Tracking Control of Nonlinear Structural and Mechanical Systems", Proceedings of the Royal Society of London, Series A, 459, pp. 1783-1800, 2003. PDF
• Udwadia, F.E., H. von Bremen, R. Kumar and M. Hosseini, “Time Delayed Control of Structural Systems,” International Journal of Earthquake Engineering and Structural Dynamics, 32, pp. 495-535, 2003. PDF
• Udwadia, F.E., and R.E. Kalaba, "Sequential Determination of the {1,4}-Inverse of a Matrix," Journal of Optimization Theory and Applications, Vol. 117, No. 1, pp. 1-7, 2003. PDF
• Udwadia, F.E., and R. E. Kalaba, "What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems?" Journal of Applied Mechanics, 69, pp. 335-339, 2002. PDF
• Udwadia, F.E., and H. von Bremen, "Computational Explorations into the Dynamics of Rings of Coupled Nonlinear Oscillators," Applied Mathematics and Computation, 129, pp. 55-85, 2002. PDF
• Udwadia, F.E., and H. von Bremen, "Computation of Lyapunov Characteristic Exponents for Continuous Dynamical Systems," Zeitschrift fur Angewandte Mathematik und Physik, 53, pp.123-146, 2002. PDF
• Udwadia, F.E., and R.E. Kalaba, "On the Foundations of Analytical Dynamics," Intl. Journ. Nonlinear Mechanics, 37, pp. 1079-1090, 2002. PDF
• Udwadia, F.E., and R. Kalaba, "Explicit Equations of Motion for Systems with Non-Ideal Constraints," Journal of Applied Mechanics, 68, pp. 462-467, 2001. PDF
• Udwadia, F.E., and H. von Bremen, "An Efficient and Stable Approach for Computation of Lyapunov Characteristic Exponents of Continuous Dynamical Systems," Applied Math. and Computation, 121, pp. 219-259, 2001. PDF
• Kalaba, R. and Udwadia, F.E., "Analytical Dynamics with Constraint Forces that Do Work," Applied Math and Computation, 121, pp. 211-217, 2001. PDF
• Udwadia, F.E., and H. von Bremen, "A Note on the Computation of the Largest p-Lyapunov Characteristic Exponents for Nonlinear Dynamical Systems," Applied Math. and Computation, 114, pp. 205-214, 2000. PDF
• Udwadia, F.E., and R. E. Kalaba, "Non-ideal Constraints and Lagrangian Dynamics," Journal of Aerospace Engineering, 13, pp. 17-22, 2000. PDF
• Udwadia, F.E., "Fundamental Principles of Lagrangian Dynamics: Mechanical Systems with Non-ideal, Holonomic, and Non-holonomic Constraints," Journ. Math. Analy. & Appl., 252, pp. 341-355, 2000. PDF
• Udwadia, F.E., and R. Kalaba, "General Forms for the Recursive Determination of Generalized Inverses," Journal of Optimization Theory and Applications, 101, pp. 509-523, 1999. PDF
• Udwadia, F.E., and R. Kalaba, "A Unified Approach for the Recursive Determination of Generalized Inverses," Comp. Math. Appl., 37, pp. 125-130, 1999. PDF
• Udwadia, F.E., and N. Raju, “Some Global Properties of a Pair of Coupled Maps: Quasi-symmetry, Periodicity, and Synchronicity,” Physica D, 111, pp. 16-26, 1998. PDF
• Udwadia, F.E., M. Hosseini and B. Wada, "Distributed Control of Large-Scale Structural Systems," Journal of Computer-Aided Civil and Infrastructure Engineering, 13, Special Issue on Structural Control, pp. 377-387, 1998. PDF
• Udwadia, F.E., and W. Proskurowski, "A Memory-Matrix-Based Identification Methodology for Structural and Mechanical Systems," Intl. Journ. Earthquake Engineering and Structural Dynamics, 27, pp. 1465-1481, 1998. PDF
• Udwadia, F.E., and R. E. Kalaba, "The Gibbs-Appell Equation and Generalized Inverse Forms," Quarterly of Applied Mathematics, 56, pp. 277-288, 1998. PDF
• Udwadia, F.E., and R. E. Kalaba, "An Alternative Proof of the Greville Formula", Journal of Optimization Theory and Applications, Vol. 94, No 1, pp.23-28, 1997 PDF
• Udwadia, F.E., Raju, N., "Dynamics of Coupled Nonlinear Maps and Its Application to Ecological Modeling", Applied Mathematics and Computation, 82, pp.137-179, 1997. PDF
• Udwadia, F.E., Hosseini, M., Chen, Y., "Robust Control of Uncertain Systems with Time Varying Delays in Control Input", Proceedings of the Americal Control Conference, 1997. PDF
• S. Beifus, W. Proskurowski and Udwadia, F.E., “A Fuzzy Logic Approach to Incorporating Managerial Thinking in Prediction and Control: a case study of market penetration,” Journal of Optimization Theory and Applications, 92, pp. 225-248, 1997. PDF
• H. Von Bremmen, Udwadia, F.E., and W. Proskurowsi, “An Efficient Method for the Computation of Lyapunov Numbers in Dynamical Systems,” Physica D, 110, pp. 1-16, 1997. PDF
• Udwadia, F.E., R. E. Kalaba, and Eun Hee-Chang, “Equations of Motion for Constrained Mechanical Systems and the Extended D’Alembert Principle,” Quarterly of Applied Mathematics, 56, pp. 321-331, 1997. PDF
• Udwadia, F.E., and N. Raju, “Dynamics of Coupled Nonlinear Maps and its Application to Ecological Modeling,” Applied Math and Computation, 82, pp. 137-179, 1997. PDF
• Udwadia, F.E., “Equations of Motion for Mechanical Systems: a unified approach,” International Journal of Nonlinear Mechanics, 31, pp. 951-958, 1996. PDF
• C. Itiki, R. Kalaba and Udwadia, F.E., “Inequality Constraints in the Process of Jumping,” Applied Mathematics and Computation, 78, pp. 163-173, 1996. PDF
• Udwadia F.E., and R. E. Kalaba, “Equations of Motion for Mechanical Systems,” Journal of Aerospace Engineering, 9, pp. 64-69, 1996. PDF
• Udwadia, F.E., R. E. Kalaba and M. Z. Nashed, “On the Existence and Uniqueness of the Solution of the Equation of Motion for Constrained Mechanical Systems,” Mathematical Problems in Engineering, 1, pp. 37-39, 1995.
• Kalaba R. E., Udwadia, F.E., and R. Xu, “The Bellman-Gauss-Vasudevan Principle of Constrained Motion,” Topics in Mathematical Physics, Allied Publishers, 1995.
• Udwadia, F.E., and R. E. Kalaba, “The Geometry of Constrained Motion,” Zeitschrift fuer Angewandte Mathematik und Mechanik, 75, pp. 637-640, 1995.
• Kalaba, R.E., Udwadia, F.E., R. Xu and C. Itiki, “The Equivalence of Lagrange's Equations of Motion of the First Kind and the Generalized Inverse Form,” Nonlinear World, 2, pp. 519-526, 1995.
• Udwadia, F.E., and R. E. Kalaba, “An Alternate Proof for the New Equations of Motion for Constrained Mechanical Systems,” Applied Math. and Computation, 70, pp. 339-342, 1995. PDF
• Udwadia, F.E., and R. Kumar, “Time-Delayed Control of Classically Damped Structural Systems,” International Journal of Control, 60, pp. 687-713, 1994.
• Xu. R, Udwadia, F.E., J. Moore and R. Kalaba, “Lagrange's Problem Without Lagrange Multipliers: The Holonomic Case,” Nonlinear World, 1, pp. 229-243, 1994. PDF
• Kalaba R. E. and Udwadia, F.E., Lagrangian Mechanics, “Gauss’s Principle and Generalized Inverses: New Equations of Motion for Nonholonomically Constrained Discrete Dynamical Systems,” Quarterly of Applied Mathematics, 52, pp. 229-242, 1994.
• Udwadia, F.E., “Methodology for Optimum Sensor Locations for Parameter Identification in Dynamic Systems,” Journal of Engineering Mechanics, 120, pp.368-390, 1994. PDF
• Udwadia, F.E., and R. Kumar, “Convergence of Iterative Methods for Non-classically Damped Dynamic Systems,” Applied Mathematics and Computation, 61, pp. 61-97, 1994. PDF
• Udwadia, F.E., and R. Kumar, “Iterative Methods for Non-Classically Damped Dynamic Systems,” International Journal of Earthquake Engineering and Structural Dynamics, 23, pp. 137-152, 1994 PDF
• Udwadia, F.E., and R. E. Kalaba, “New Approaches to the Control of Mechanical Systems,” Mechanics and Control, Los Angeles, Plenum Press, 1993.
• Udwadia, F.E., and R. E. Kalaba, “On Motion,” Journal of the Franklin Institute, 330, pp. 571-577, 1993.PDF
• Kalaba, R.E. and Udwadia, F.E., "Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss's Principle", Journal of Applied Mechanics, Vol. 60(3), pp. 662-668, 1993. PDF 
• Kalaba, R.E., and Udwadia, F.E., “An Associative Memory Approach to the Rapid Identification of Nonlinear Structural and Mechanical Systems,” Journal of Optimization Theory and Applications, 76, pp. 207-223, 1993.
• Udwadia, F.E., “Further Results on the Iterative Solution of Nonclassically Damped Linear Dynamic Systems,” Journal of Applied Mechanics, 60, pp. 235-239, 1993.
• Kalaba, R.E., and Udwadia, F.E., “On Constrained Motion,” Applied Mathematics and Computation, 51, pp. 85-86, 1992.
• Udwadia, F.E., “Noncollocated Control of Distributed-Parameter Nondispersive Systems with Tip Inertias Using Time Delays,” Applied Mathematics and Computation, 47, pp. 47-75, 1992, PDF.
• Udwadia, F.E., “Intelligent Control of Tall Building Structures Subjected to Strong Earthquake Ground Shaking,” Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Spain, July 14-19, 1992.
• Udwadia, F.E., and R. E. Kalaba, “A New Perspective on Constrained Motion,” Proceedings of the Royal Society of London, Series A, 439, November, pp. 407-410, 1992. PDF
• Udwadia, F.E., “Non-collocated Control of Continuous Systems with Tip-Inertias,” Applied Mathematics and Computation, 47, pp. 47-75, 1992.
• Udwadia, F.E., “Some Convergence Results Related to JOR Iterative Schemes used in Structural Mechanics Dealing with Positive-Definite Symmetric Matrices,” Applied Mathematics and Computation, 47, pp. 37-45, 1992.
• Udwadia, F.E., "Noncollocated Point Control of Nondispersive Distributed-Parameter Systems Using Time Delays," Applied Mathematics and Computation, Vol. 42, pp. 23-63, 1992. PDF
• Udwadia, F.E.,and Esfandiari, R. S., "Nonclassically Damped Dynamic Systems: An Iterative Approach"; Journal of Applied Mechanics, Vol. 57, No. 2, pp. 423-433, 1990. PDF
• Udwadia, F.E., "Some Results on Maximum Entropy Distributions for Parameters Known to Lie in Finite Intervals," SIAM Review, Vol. 31, No. 1, pp. 103-109, 1989. PDF
• Guttalu, R., Udwadia, F.E.,"Period Three May not Mean Chaos: An Example of a Piecewise Linear Map," Computational Mechanics, Vol. 5, pp. 113-118, 1989. PDF
• Udwadia, F.E., "Chaotic Dynamics of a Piecewise Cubic Map", Physical Review A, Vol. 40, No. 7, pp. 4032-4044, 1989. PDF
• Udwadia, F.E., Flashner, H., "Tradeoffs Between Identification and Control in Dynamical Systems," Journal of Applied Mechanics, Vol. 55, pp. 939-944, 1988. PDF
• Udwadia, F.E., "Uniqueness in the Identification of Building Structures from Forced Vibration Tests," Transactions of the CSME, Vol. 9, No. 1, pp. 19-25, 1985. PDF
• Udwadia, F.E., Shah, P. C., "Uniqueness of Damping and Stiffness Distributions in the Identification of Soil and Structural Systems", Journal of Applied Mechanics, 1978. PDF
• Shah, P. C., Udwadia, F.E.,"A Methodology for Optimal Sensor Locations for Identification of Dynamic Systems", Journal of Applied Mechanics, 45, pp. 188-196, 1978. PDF
• Udwadia, F.E., and Sharma, D., "Some Uniqueness Results Related to Building Structural Identification", SIAM J. Appl. Math.,34, 1, 1978. PDF
• Udwadia, F.E., and Shah, P. C., "Identification of Structures Through Records Obtained During Strong Earthquake Ground Motion", Journal of Engineering for Industry, 1976. PDF
• Marmarelis, P.Z., and Udwadia, F.E., "The Identification of Building Structural Systems II. The Nonlinear Case", Bulletin of the Seismological Society of America, Vol. 66, No. 1, pp. 153-171, February 1976. PDF 
• Udwadia, F.E., and Marmarelis, P.Z., "The Identification of Building Structural Systems I. The Linear Case", Bulletin of the Seismological Society of America, Vol. 66, No. 1, pp. 125-151, February 1976. PDF 
• Udwadia, F.E., and Trifunac, M.D., "Time and Amplitude Dependant Response of Structures", Earthquake Engineering and Structural Dynamics, Vol. 2, pp. 359-378, 1974. PDF