Firdaus Udwadia: Selected Recent Publications in Science & Engineering    

• Udwadia, F., Farahani, A., "Accelerated Runge-Kutta Methods", Discrete Dynamics in Nature and Society, Vol. 2008, Article ID 790619, 38 pages, 2008. PDF 
• Udwadia, F. "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., Nakanishi, J., Schaal, S., "A Unifying Framework for Robot Control with Redundant DOFs", Auton Robot, Vol. 24 , pp. 1-12, 2008. PDF 
• Udwadia, F., 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 
• Firdaus E. Udwadia, Hubertus von Bremen, Phailaung Phohomsiri, "Time-delayed Control Design for Active Control of Structures: Principles and Applications," Struct. Control Health Monit., 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, 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. 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, pp. 1-21, March 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,” Intl. Journ. 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?" Journ. 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 Math. 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 F. Udwadia, "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
• 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, 1997. PDF
• S. Beifus, W. Proskurowski and F. E. Udwadia, “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, F. E. Udwadia and W. Proskurowsi, “An Efficient Method for the Computation of Lyapunov Numbers in Dynamical Systems,” Physica D, 110, pp. 1-16, 1997. PDF
• C. Itiki, R. Kalaba and F. E. Udwadia, “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., F. E. Udwadia 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.
• R. Kalaba, F. Udwadia, 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, F. E. Udwadia, 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 F. E. Udwadia, 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.
• Kalaba R. E. and F. E. Udwadia, “Equations of Motion for Non-holonomically Constrained Discrete Dynamical Systems,” Journal of Applied Mechanics, 60, pp. 662-668, 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., “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 F. E. Udwadia, “On Constrained Motion,” Applied Mathematics and Computation, 51, pp. 85-86, 1992.
• Udwadia, F., “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. "A Methodology for Optimal Sensor Locations for Identification of Dynamic Systems", Journal of Applied Mechanics, 45, pp. 188-196, 1978. PDF
• Udwadia, F. E., Sharma, D., "Some Uniqueness Results Related to Building Structural Identification", SIAM J. Appl. Math.,34, 1, 1978. PDF
• Udwadia, F. E., Shah, P. C., "Identification of Structures Through Records Obtained During Strong Earthquake Ground Motion", Journal of Engineering for Industry, 1976. PDF