A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

Foreword Preface to the Second Edition Preface 1. Maximization, Minimization, and Motivation 2. Vectors and Matrices 3. Diagonalization and Canonical Forms for Symmetric Matrices 4. Reduction of General Symmetric Matrices to Diagonal Form 5. Constrained Maxima 6. Functions of Matrices 7. Variational Description of Characteristic Roots 8. Inequalities 9. Dynamic Programming 10. Matrices and Differential Equations 11. Explicit Solutions and Canonical Forms 12. Symmetric Function, Kronecker Products and Circulants 13. Stability Theory 14. Markoff Matrices and Probability Theory 15. Stochastic Matrices 16. Positive Matrices, Perron's Theorem, and Mathematical Economics 17. Control Processes 18. Invariant Imbedding 19. Numerical Inversion of the Laplace Transform and Tychonov Regularization Appendix A. Linear Equations and Rank Appendix B. The Quadratic Form of Selberg Appendix C. A Method of Hermite Appendix D. Moments and Quadratic Forms Index.

Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)

This work describes a new type of efficiency attack that can be used to degrade the performance of automated vehicular transportation systems. Next-generation transportation technologies will leverage increasing use of vehicle automation. Proposed vehicular automation systems include cooperative adaptive cruise control and vehicle platooning strategies which require cooperation and coordination among vehicles. These strategies are intended to optimize through-put and energy usage in future highway systems, but, as we demonstrate, they also introduce new vulnerabilities. In this work we show that a typical platooning system would allow a maliciously controlled vehicle to exert subtle influence on the motion of surrounding vehicles. This effect can be used to increase the energy expenditure of surrounding vehicles by 20% to 300%.

CPS: an efficiency-motivated attack against autonomous vehicular transportation

Are the eigensolutions of a 1-d.o.f. system with viscoelastic damping oscillatory or not?

We analytically investigate the stability of a discrete viscoelastic system with negative stiffness elements both in the time and frequency domains. Parametric analysis was performed by tuning both the amount of negative stiffness in a standard linear solid and driving frequency. Stability conditions were derived from the analytical solutions of the differential governing equations and the Lyapunov stability theorem. High frequency response of the system is studied. Stability of singularities in the dissipation tan 6 is discussed. It was found that stable singular tan δ is achievable. The system with extreme high stiffness analyzed here was metastable. We established an explicit link for the divergent rates of the metastable system between the solutions of differential governing equations in the time domain and the Lyapunov theorem.

/pdf/stability-of-negative-stiffness-viscoelastic-systems-eav6am401e.pdf

Stability of negative stiffness viscoelastic systems

A sufficient condition for instability of equilibrium of non-conservative undamped systems

The stability of linear potential gyroscopic systems when the potential energy has a maximum

The paper investigates the stability of a linear mechanical system subjected to potential and circulatory forces. Three theorems which provide stability conditions directly in terms of the coefficient matrices are established.

On the stability of linear circulatory systems

A criterion which contains necessary and sufficient conditions for spectral stability, flutter and divergence instability of circulatory systems is formulated. The conditions are expressed via the properties of a quadratic form with the coefficients expressed by means of the traces of powers of the non-conservative stiffness matrix. As corollaries, this general algebraic result leads to a number of stability conditions known in the literature.

Ranislav M. Bulatovic

Papers

A sufficient condition for instability of equilibrium of non-conservative undamped systems

The stability of linear potential gyroscopic systems when the potential energy has a maximum

On the stability of linear circulatory systems

A stability criterion for circulatory systems

On the critical damping in multi-degree-of-freedom systems