Collisions in Classical Mechanics in Terms of Mass-Momentum “Vectors” with Galilean Transformations

We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.

Influence of viscous force on the dynamic process of micro-sphere in optical tweezers

With the advantages of noncontact,high accuracy,and high flexibility,optical tweezers hold huge potential for micro-manipulation and force measurement.However,the majority of previous research focused on the state of the motion of particles in the optical trap,but paid little attention to the early dynamic process between the initial state of the particles and the optical trap.Note that the viscous forces can greatly affect the motion of micro-spheres.In this paper,based on the equations of Newtonian mechanics,we investigate the dynamics of laser-trapped micro-spheres in the surrounding environment with different viscosity coefficients.Through the calculations,over time the particle trajectory clearly reveals the subtle details of the optical capture process,including acceleration,deceleration,turning,and reciprocating oscillation.The time to equilibrium mainly depends on the corresponding damping coefficient of the surrounding environment and the oscillation frequency of the optical tweezers.These studies are essential for understanding various mechanisms to engineer the mechanical motion behavior of molecules or microparticles in liquid or air.

Conservative Vector Fields and the Intersect Rule

This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued potential function. Gradient fields are irrotational, as in the curl in all conservative vector fields is zero, by Clairaut’s Theorem. Additionally, line integrals in conservative vector fields are path-independent, and line integrals over closed paths are always equal to zero, properties proved by the Gradient Theorem of multivariable calculus. Gradient fields represent conservative forces, and the associated potential function is analogous to potential energy associated with said conservative forces. The Intersect Rule provides a new, unique shortcut for determining if a vector field is conservative and deriving potential functions, by treating the indefinite integral as a set of infinitely many functions which satisfy the integral.

Theory of Gravitons in Spiral and Dwarf Galaxy Rotation Curves

We hypothesize that gravitons contribute significantly to the process that flattens galaxy rotation curves. Gravitons travelling against a gravitational field experience an energy loss due to gravitational redshift identical to the effect on light. This energy loss requires an increased rotational velocity to stabilize a galaxy. We will show that this approach successfully explains the rotational properties of spiral and dwarf galaxies.

The Contribution of the Gravitational Propagation Delay to Orbital and Center of Mass Motions

Recent measurements have shown that gravitational waves and thus the gravitational interaction propagate with the speed of light. The propagation delay of the gravitational interaction in orbiting systems couples the orbital and center of mass motions. This causes the orbits to spiral out and the center of mass to accelerate. It is one of a number of small effects modifying the Kepler orbits. The calculations show that the analytical describable expansion of the semimajor axis started at a time that is less than the age of the systems. This could be caused by a collision of a system component in the past. The effect of this propagation delay on the motion of the Earth Moon and the Brown Dwarf 569Bab binary star system is analyzed. These systems were chosen because a considerable amount of measured astronomical data is available. The calculated results are in excellent agreement with the measured data. In galaxies, too, the energy transfer from the orbit of the star cloud to the center of mass motion causes the galaxies to ac-celerate. If galaxies are considered to be molecules of the universe, then the acceleration of the galaxies will cause the molecular gas to heat and expand. Alternatively, the loss in orbital internal energy of the galaxies should be included in the mass and energy in the calculation of the expanding Universe.

A Second Discussion on Cosmic Space in Zero Dimension <br/>—A Discussion on Spatial Questions According to Classical Physics

Since their publications, theories in classical and modern physics have thoroughly studied the essence of matters. However, modern physical models only examined the change on the appearance of substances within its surrounding space, and it has never involved the study of absolute space as models in modern physics did not endorse the existence of absolute space. This work put in question the theories of higher-dimensional Universe accepted in mainstream physics. In order to reignite discussions in the Essence of the Universe, the author proposed the hypothesis that the Essence of the Universe is the zero-dimensional space and that it does not change accordingly with the change in substances, and that space is only and solely space. This work explored the topic of a zero-dimensional Universe using Western and Eastern philosophical concepts and their derivatives. This work concluded that zero-dimensional space could be a possibility that should be further studied, that the cause and information of Intelligent Energy proposed by the author influenced the motion and change of substances, and that time and force were merely parameters that describe the state of matters.