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For musical sense, see Dynamics (music) .
The dynamic is part of physics that describes the evolution over time of a physical system in relation to the causes of changes physical and / or state of motion. The aim is to describe the dynamics of the factors that may cause alterations of a physical system, quantify and propose equations of motion or evolution equations for this system.
The study of the dynamics is prominent in the mechanical systems (classical, relativistic or quantum), but also thermodynamics and electrodynamics . In this paper we develop the main aspects of the dynamics of mechanical systems, leaving for other items to study the dynamics in non-mechanical. Content
[ hide] 1 History
2 Calculus 2.1
dynamic conservation laws
2.2 Equations of Motion
3 Dynamics of mechanical systems
3.1 Particle Dynamics
3.2 Dynamics Rigid body
4 Concepts related to the dynamic inertia
4.1 4.2 Work and Energy
5 See also
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History [edit ]
The first major contribution is Galileo Galilei because . His experiments led to uniformly accelerated bodies Isaac Newton to formulate its fundamental laws of motion, which he presented in his major work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy ") in 1687 .
Scientists believe current laws that made Newton give the correct answers to most of the problems of moving bodies, but there are exceptions. In particular, the equations to describe the motion are not adequate when a body travels at high speeds with regard to the speed of light or when objects are extremely small size comparable to molecular sizes.
Understanding the laws of classical dynamics has allowed man to determine the value and direction of the force to be applied to produce a particular movement or change in the body. For example, to make a rocket away from Earth, apply a certain force to overcome the force of gravity that attracts them in the same way, for a given load transport mechanism is necessary to apply adequate force in the right place.
dynamic Calculus [edit ]
Through the concepts of displacement , speed and acceleration is possible to describe the movements of a body or object without considering how they were made, discipline known for cinematic . By contrast, the dynamic is part of the mechanical that deals with the study the movement of bodies under the action of forces .
The dynamic analysis approach is based on the equations of motion of and integration. For extremely simple problems using equations of Newtonian mechanics directly aided the conservation laws .
conservation laws [edit ]
Main article:
conservation law Conservation laws can be formulated in terms of theorems that establish specific conditions under which a particular magnitude "is preserved" (Ie, remains constant in value over time as the system moves or changes over time). Besides the law of conservation of energy other important conservation laws take the form of theorems vector. These theorems are:
theorem of momentum, which for a system of point particles requires particle forces only depend on the distance between them and are directed along the line that connects them. In continuum mechanics and rigid body mechanics vector can be formulated theorems of momentum conservation.
The angular momentum theorem states that under conditions similar to the previous theorem vector sum of torques about an axis is equal to the temporal variation of angular momentum .
Equations of Motion [edit ]
Main article:
equation of motion there are several ways to raise equations of motion to predict the evolution in time of a mechanical system based on the initial conditions and acting forces. In classical mechanics there are several possible formulations to propose equations:
The that uses Newtonian mechanics to write directly ordinary differential equations of second order in terms of forces and in Cartesian coordinates. This system leads to difficult equations integrable by elementary means and is only used in very simple problems, usually using inertial reference systems. The Lagrangian mechanics
, this method also uses ordinary differential equations of second order, while allowing the use of fully general coordinates, called generalized coordinates , better adapted to the geometry of the problem. In addition the equations are valid in any reference frame it is inertial or not. Besides getting easier to integrate the systems Noether theorem and the coordinate transformations can find comprehensive movement, also called conservation laws, more easily than the Newtonian approach. The Hamiltonian mechanics
is similar to above but in the equations of motion are ordinary differential equations are first order. Moreover, the range of admissible coordinate transformations is much wider than in Lagrangian mechanics, which makes it even easier to find integrals of motion and conserved quantities.
The Hamilton-Jacobi method is a method based on the resolution of a partial differential equation using the method separation of variables, which is the easiest way when you know the right set of integrals of motion.
Dynamics of mechanical systems [ edit]
In physics there are two major types of physical systems finite systems of particles and fields . The evolution over time of the first can be described by a finite set of ordinary differential equations, why is said to have a finite number of degrees of freedom . In contrast, the evolution over time of the fields requires a set of complex equations. Partial, and in some informal sense behave like a particle system with an infinite number of degrees of freedom.
Most mechanical systems are the first type, although there are mechanical systems which are described more simply as fields, as with fluid or deformable solid . It also happens that some mechanical systems ideally formed by an infinite number of particles, such as rigid bodies can be described by a finite number of degrees of freedom.
particle dynamics [edit ]
Main article: Dynamics of material point
The dynamics of the particle is a part of Newtonian mechanics in which the systems are analyzed as systems of point particles and distance forces are exerted snapshots
rigid body dynamics [edit ]
Main article: rigid body mechanics
The mechanics of a rigid body is that which looks for movement and balance of solid material deformation ignoring their . It is, therefore, a mathematical model useful to study some of the mechanics of solids, since all real solids are deformable. Rigid means a set of points in space that move in such a way that does not alter the distances between them, whatever the force acting (mathematically, the motion of a rigid body is given by a group of isometries uniparametrical) .
Concepts related to the dynamics [edit ]
Inertia [edit ]
Main articles: inertia and inertial mass
Inertia is the difficulty or resistance opposing a physical system or a social system to change.
In physics we say that a system has more inertia when it is more difficult to change in the physical state of the same. The two most common uses in physics are the mechanical inertia and thermal inertia. The first one appears in mechanics and is a measure of difficulty to change the state of motion or rest of a body. The mechanical inertia depends on the amount of mass and inertia tensor. Thermal inertia measures the difficulty with which a body changes its temperature by contact with other bodies or to be heated. The thermal inertia depends on the amount of mass and heat capacity.
Calls inertial forces are fictitious forces and apparent that an observer in a non-inertial reference ....
Inertial mass is a measure of mass resistance to the change in speed relative to an inertial reference system. In classical physics the inertial mass of point particles is defined by the following equation, where a particle is taken as the unit (m1 = 1):
where I is the inertial mass of the particle i, and the acceleration ai1 i initial particle in the direction of the particle i to particle 1 in a volume occupied only by particles i 1, where two particles are initially at rest at a distance unit. No external forces but exert force particles into each other.
Work and Energy [edit ]
The work and energy displayed on the mechanics through energy theorems. The primary, and from which they derive the other theorems, the theorem energy. This theorem can be stated in differential version or full version. Henceforth we will refer to the Theorem of kinetic energy as TEC. Thanks to the TEC
can establish a relationship between mechanics and other
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