Feynman's Proof of the Lorentz Force Equations with Dissipation Linear in the Velocity

1997 ◽  
Vol 12 (33) ◽  
pp. 2523-2533
Author(s):  
S. K. Soni ◽  
Simmi Singh
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Lorentz Force ◽  
Linear Dependence ◽  
Velocity Vector ◽  
Equations Of Motion ◽  
Type Form ◽  
Helmholtz Conditions ◽  
Dissipative Terms ◽  
Lorentz Force Law

We present the Feynman proof of the Lorentz force law plus dissipative terms with a linear dependence on the velocity vector. In addition, we discuss in this context the inverse problem of the calculus of variations and the inverse problem for the Poisson dynamics. Given the equations of motion, the Helmholtz conditions for the inverse problem of the calculus of variations are solved and the Lagrangian is shown to have the nonsingular gauge type form.

scholarly journals Some Further Remarks on Hamilton’s Principle

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Firdaus E. Udwadia ◽  
George Leitmann ◽  
Hancheol Cho
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Equations Of Motion ◽  
Hamilton’S Principle ◽  
Hamilton's Principle

This paper deals with the inverse problem of finding a suitable integrand so that upon the use of the calculus of variations, one obtains the equations of motion for systems in which the forces are nonpotential. New extensions and generalizations of previous results are obtained.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

2021 ◽  
Author(s):  
Vahid Mohamadhashemi ◽  
Amir Jalali ◽  
Habib Ahmadi
Keyword(s):  
Carbon Nanotube ◽  
Velocity Vector ◽  
Multiple Scales ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Maximum Amplitude ◽  
Beam Theory ◽  
Physical Parameters ◽  
Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

Investigation on Laminar Flow Field Performances in a Dual-Impeller Stirred Tank

2012 ◽  
Vol 550-553 ◽  
pp. 2964-2967
Author(s):  
De Yu Luan ◽  
Shen Jie Zhou ◽  
Song Ying Chen
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Radial Velocity ◽  
Velocity Vector ◽  
Equations Of Motion ◽  
Stirred Tank ◽  
Field Pattern ◽  
3D Flow ◽  
Multiple Reference

Abstract: The 3D flow field generated by a dual-impeller in the agitation of glycerin fluid was simulated using the commercial CFD package. The flow was modeled as laminar and a multiple reference frame (MRF) approach was used to solve the discretized equations of motion. The velocity profiles with a dual-impeller rotating at constant speed of 200r/min and at different layer clearances were obtained. By analysis to their axial and radial velocity vector plots and velocity distribution curves, it is found that the velocity distributions of the dual 6-bladed radial disc turbines (2-6DT) are better when the clearance is bigger or equal to the T/2, accompanied with the flow field pattern of parallel flow. Moreover，when the clearance is smaller or equal to the T/3, there are more advantages for 6-bladed radial disc turbines + pitch 4-bladed turbines (6DT+PTB) than other combinations，followed by the flow field pattern of connected flow.

Flexible Valveless Pump for Bio Applications

2019 ◽  
Author(s):  
Masoud Naghdi ◽  
Farhad Farzbod ◽  
Paul M. Goggans
Keyword(s):  
Liquid Metal ◽  
Lorentz Force ◽  
Permanent Magnets ◽  
Mechanical Energy ◽  
Electrical Energy ◽  
Electrical Current ◽  
Electromechanical Actuators ◽  
Valveless Pump ◽  
Metal Wires ◽  
Lorentz Force Law

Abstract In electromechanical actuators Lorentz force law is used to convert electrical energy into rotational or linear mechanical energy. In these conventional electromechanical actuators, rigid wires conducts the electrical current and as such the types of motion generated by these actuators are limited. Recent advances in liquid metal alloys permit designing electrical wires that are stretchable. These flexible wires have been used to fabricate various flexible connections, sensors and antennas. However, there have been very little efforts to use these stretchable liquid metal wires as actuators. Building upon our previous work in this area, we have made a flexible pump which can be used in bio applications. In this design we placed a flexible polymeric substrate filled by liquid metal Galinstan between two permanent magnets. Since the pump should convey the biological cells suspended along the fluid flow, utilizing check valves may increase the risk of clog in the inlet or outlet. Therefore, our design is based on the nozzle/diffuser concept. This new pump can be considered as a peristaltic and valve-less mechanical pumps which utilizes the Lorentz force law as the actuating mechanism.

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