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The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, [ 1 ] but they have also been developed for the study of the mechanics of deformable bodies.
The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Technically, quantum field theory provides the mathematical framework for the Standard Model, in which a Lagrangian controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical field that pervades space-time. [51]
For a system of particles with masses , with coordinates = that constitute a time-dependent random variable, the resulting Langevin equation is [2] [3] ¨ = ˙ + (), where () is the particle interaction potential; is the gradient operator such that () is the force calculated from the particle interaction potentials; the dot is a time derivative ...
The reconciliation of gravity to the current particle physics theory is not solved; many theories have addressed this problem, such as loop quantum gravity, string theory and supersymmetry theory. Practical particle physics is the study of these particles in radioactive processes and in particle accelerators such as the Large Hadron Collider.
The mathematical definition of particle methods captures the structural commonalities of all particle methods. [6] It, therefore, allows for formal reasoning across application domains. The definition is structured into three parts: First, the particle method algorithm structure, including structural components, namely data structures, and ...
Nauenberg worked in the field of particle and nuclear physics as well as theoretical solid state physics, astrophysics and nonlinear dynamics. His most-cited result, [3] written in collaboration with Nobel laureate Tsung-Dao Lee, is the Kinoshita-Lee-Nauenberg theorem (KLN theorem). Since the 1990s, he has published numerous works on the ...