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A few preliminary fundamentals
Published in Paolo Luciano Gatti, Advanced Mechanical Vibrations, 2020
Since the motion of a point particle necessarily occurs in time, it is natural to describe it by means of an appropriate function of time, say x(t), whose physical meaning and units depend on the scope of the analysis and, in applications, also on the available measuring instrumentation. Having already pointed out above that our main interest lies in oscillations about an equilibrium position, the simplest case of this type of motion is called harmonic and is mathematically represented by a sine or cosine function of the form x(t)=Xcos(ωt−θ)
Modeling with Partial Differential Equations
Published in Mayer Humi, Introduction to Mathematical Modeling, 2017
IdealizationsWe assume that the concept of a point mass is valid. As a matter of fact, we note that due to the discrete nature of matter, the notion of a (mathematical) point particle with mass m has no physical meaning.We assume that the field generated by a point particle does not act on itself; otherwise, various contradictions will creep in.
Vectors
Published in Jamal T. Manassah, Elementary Mathematical and Computational Tools For Electrical and Computer Engineers Using Matlab®, 2017
Newton’s second law of classical motion states that the force on a point particle is equal to its mass multiplied by its acceleration: F→=ma→
Berry phase of the linearly polarized light wave along an optical fiber and its electromagnetic curves via quasi adapted frame
Published in Waves in Random and Complex Media, 2022
Talat Körpinar, Rıdvan Cem Demirkol
If the motion of the linearly polarizable point-particle corresponds to an -curve along with the optical fiber in the 3D space the angular momentum or mechanical angular momentum of the linearly polarizable point-particle along with the optical fiber in the 3D space is given by using Equations (45)–(47) as the following way Here, one can easily induce that the magnitude of the angular momentum of the polarizable point-particle along with the optical fiber in the 3D space is Finally, we reach to the point where the magnetic moment of the linearly polarizable point-particle along with the optical fiber in the 3D space is written as a vector field due to Equation (49) All these results include the behavior of the linearly polarizable point-particle along with the optical fiber in the 3D space with spin in a magnetic field . Hence, linearly polarizable point-particle experiences the torque from Equations (46) and (51) given by the following identity In Hence, it is found that the sum of externally applied net torque on the linearly polarizable point-particle is zero. It implies that the particle is in rotational equilibrium in the 3D space.