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Brownian Motion and Levy Processes, Nonlinear Filtering Plasma Waves, Quantum Stochastics and Parameter Estimation
Published in Harish Parthasarathy, Electromagnetics, Control and Robotics, 2023
Likewise the time component of the four force density is F0=J.E=(E,∇×B)/μ0−ε0(E,E,0)=−∇(E×B)/μ0−(B,B,0)/μ0−ξ0(E,E,0)=−S,α0α
Fundamentals of Losses
Published in Kenji Uchino, High-Power Piezoelectrics and Loss Mechanisms, 2020
Figure 3.15c describes: The output displacement u(t) is delayed from the input force f(t). The phase delay ϕ in the above equation is negative!Spring force is opposite to the displacement.Damping force is delayed 90° from the displacement and opposite to the velocity.Inertial force is in phase with the displacement and opposite to the acceleration.Four force vectors rotate at the angular velocity ω, by keeping the relative position fixed.
Novel Relativity Theories of Synthetic Aperture Radar
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
Furthermore, an inertial SAR reference frame in relative motion with the moving frame of the oil-covered dynamic sea-state measures a period dilated by the γ Lorentz factor. If one wants to compute the time dilation in the oscillator period of oil-covered as imaged by the SAR moving frame, we must consider γ factor, which is attached to the rest mass of the oil-covered and a second γ factor inversely attached to the dynamic of the sea-state. The latter is due to the definition of the four-force in special relativity. Needless to say, moving objects appear to experience the length contraction because they are perceived in space-time cross-section. In this sense, the length contraction is considered as some sort of optical illusion depending on the sensor. It is only meant to emphasize that length contraction appears differently in various SAR frames, as verified by reasonable coordinates.
Origami-inspired structures with programmable multi-step deformation
Published in Mechanics of Advanced Materials and Structures, 2022
Haozhe Wang, Yulong He, Anfeng Yu, Xin Li, Meng Gu, Xiaodong Ling, Guoxin Chen
Different to the CC3 and SM4, there is a competition between the structural gradient and the wall thickness gradient for CC4 and DM4 as show in Figures 18(c), 18(d), 19(e), and 19(f). It can be found that some gradient origami structures have only one force-displacement stage. This is the result of the interaction between the structural gradient and the thickness gradient. In addition, Figures 18(d) and 19(f) show that the number of force-displacement stages varies between 1 and 4 for the DM4. This is due to the following two factors: (1) Asymmetry of the upper and lower parts of the structure, resulting in asymmetry of the boundary constraints. (2) The interaction between the thickness gradient of the upper and lower parts of the structure and the structural gradient. Here, some DM4 with the same thickness have four force-displacement stages. This is caused by the boundary condition and the order of the unit cell with muti-layers. Therefore, the competition relationship is different between the structural gradient and the wall thickness gradient for CC4 and DM4, while both CC4 and DM4 have two structural gradients and two thickness gradients.
Alternative upper configurations during agility-based movements: part 1, biomechanical performance
Published in Footwear Science, 2021
Moira K. Pryhoda, Rachel J. Wathen, Jay Dicharry, Kevin B. Shelburne, Daniel Feeney, Kathryn Harrison, Bradley S. Davidson
Before performing the court-based movements, each athlete was outfitted with 38 reflective markers (22 single markers and four clusters of four markers), including a full lower extremity marker set and an abbreviated HAT segment (head, arms, trunk) marker set. An eleven-camera passive motion capture system (Vicon Motion Systems) was used to capture full body segment motion at 100 Hz using Vicon Nexus Capture software (Motion Systems Ltd, Oxford, UK). Ground reaction force information was sampled at 1000 Hz from four force platforms (Bertec, Columbus, OH). Marker data were filtered using a 4th order zero-phase-lag low-pass Butterworth filter (10 Hz cutoff). Ground reaction forces were filtered using a 4th order zero-phase-lag low-pass Butterworth filter (30 Hz cutoff).
A single-leg standing test evaluation system for fall prevention in workers
Published in Advanced Robotics, 2022
Hayato Mikami, Mami Sakata, Keisuke Shima, Tomoyuki Nagara, Makiko Yamashita, Koji Shimatani
Foot pressure and COP were measured using a Balance Wii Board. The Balance Wii Board had four force sensors at the corners. When the weights of each sensor were defined , , and , and the total weight was W, the COP value was calculated as follows: These features were used to evaluate whether the subject could stand up and the degree of wobbliness during standing up.