Parabolic Detection Algorithm of Tennis Serve Based on Video Image Analysis Technology

At present, the existing algorithm for detecting the parabola of tennis serves neglects the pre-estimation of the global motion information of tennis balls, which leads to great error and low recognition rate. Therefore, a new algorithm for detecting the parabola of tennis service based on video image analysis is proposed. The global motion information is estimated in advance, and the motion feature of the target is extracted. A tennis appearance model is established by sparse representation, and the data of high-resolution tennis flight appearance model are processed by data fusion technology to track the parabolic trajectory. Based on the analysis of the characteristics of the serve mechanics, according to the nonlinear transformation of the parabolic trajectory state vector, the parabolic trajectory starting point is determined, the parabolic trajectory is obtained, and the detection algorithm of the parabolic service is designed. Experimental results show that compared with the other two algorithms, the algorithm designed in this paper can recognize the trajectory of the parabola at different stages, and the detection accuracy of the parabola is higher in the three-dimensional space of the tennis service.

Galileo and the Law of Fall

Galileo broke away from Aristotle’s incorrect theories of motion towards his own based on experimental evidence. He employed experimentation to discover the parabolic trajectory of projectile motion and also the Law of Fall. His work helped establish the scientific method and launch the scientific revolution.

Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms

The problem of the trajectory-tracking and vibration control of highly flexible planar multi-links robot arms is investigated. We discretize the links according to the Hencky bar-chain model, which is an application of the lumped parameters techniques. In this approach, each link is considered as a kinematic chain of rigid bodies, and suitable springs are added in order to model bending resistance. The control strategy employed is based on an optimal input pre-shaping and a feedback of the joint angles to treat the effects of undesired disturbances. Some numerical examples are given to show the potentialities of the proposed control, and a comparison with a standard collocated Proportional-Derivative (PD) control strategy is performed. In particular, we study the cases of a linear and a parabolic trajectory with a polynomial time law chosen to minimize the onset of possible vibrations.

On the Shoulders of Giants

Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley. The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes. Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics. Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mourning the death of his mistress Emilie du Chatelet, the lone female French physicist of the eighteenth century.

The Measure of Life

This final topic of the book extends the ideas of dynamics in abstract spaces of high dimension to encompass the idea of a trajectory of life. Health and disease become dynamical systems defined by all the proteins and nucleic acids that comprise the physical self. Concepts from network theory, autonomous oscillators and synchronization contribute to this viewpoint. Healthy trajectories are like stable limit cycles in phase space, but disease can knock the system trajectory into dangerous regions of health space, as doctors turn to new developments in personalized medicine try to return the individual to a healthy path. This is the ultimate generalization of Galileo’s simple parabolic trajectory.

Flight of the Swallows

The science of modern dynamics takes the simple idea of Galileo’s parabolic trajectory and generalizes it into abstract hyperspaces of multiple dimensions. This chapter introduces the new way that physicists and mathematicians visualize dynamical systems, taking a global view of complex behavior and finding that the laws of physics capture the orbits of planets around suns (and the paths of light around black holes) as easily as the evolution of new species or the rise and fall of economies. This new visualization uses phase space to capture the global behavior of complex systems. The path across life, the universe and so many hyperdimensional worlds is being captured by new disciplines within new sciences like chaos theory, entanglement, network science, econophysics and evolutionary dynamics.

Epilogue: Galileo at Home in the Multiverse

This final short chapter sums up the topics of the book, showing how Galileo’s simple parabolic trajectory has matured into an overarching and grand concept that encompasses modern dynamics. Galileo achieved immortality despite his house arrest and despite the banning of his books that he feared had erased his legacy. Ironically, his house arrest gave him time to assemble and record his lifelong investigation into the science of motion—and banning his books made them immensely popular.

Galileo’s Trajectory

This chapter describes the history of Galileo’s discovery of the law of fall and the parabolic trajectory, beginning with early work on the physics of motion by predecessors like the Oxford Scholars, Tartaglia and the polymath Simon Stevin who dropped lead weights from the leaning tower of Delft three years before Galileo dropped lead weights from the leaning tower of Pisa. The story of how Galileo developed his ideas of motion is described in the context of his studies of balls rolling on inclined plane and the surprising accuracy he achieved without access to modern timekeeping. Motion was always on Galileo’s mind. He saw motion in his father’s stringed instruments, vibrating in rational resonances. He saw motion in the lantern high above in the Duomo di Pisa, swinging with fixed regularity.