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Material point: is a body whose dimension may be disregarded in the certain conditions. (ex: the study of motion of earth around the sun)
Mechanical system: an ensemble of point particles, whose motion can be free or limited by certain constraints.
Scalar field: let consider a domain in space. If a certain number U(M),where U is a scalar field, can be attributed to each point M of the domain then we say that there is a scalar field defined in the domain Ω.
Vectorial field: let consider a domain in space. If a certain vector (M),where (M) is a vector function, can be attributed to each point M of the domain then we say that there is a vectorial field defined in the domain Ω.
Referance frame: a set of coordinates relative to which the position of a material point in space can be determined and a watch for time measurement.
Inertial reference frame: a reference frame which is at rest or is moving with constant velocity, in the absence of many external field.
Inertia: the property of remaining at rest or continuing to move in a straight line at a constant speed.
Rigid body: a system of particles with constant distances between them.
Translation motion of a rigid body: is such a motion in which the line connecting any 2 particles of the body remains parallel to itself.
Rotation motion of a rigid body about a fixed vertical axis: Let consider a rigid body that can rotate about a fixed axis. Rotation of rigid body is such a motion in which the trajectories of all the points of the body are circles whose centres are located on a common straight line called axis of rotation.
Degrees of freedom: the number of independent possible motions of the system motion of the system particles. Is equal with the number of independent quantities needed to determine the system position in space.
Constraints: restrictions of geometric or kinematic nature that may be imposed on the position and velicities of a system’s particles.
Generalized coordinates: the independent parameters q1, q2… qf that determine the position of a mechanical system in space.
Generalized velocity: the time derivatives of the generalized coordinates 1, 2 …… f .
The flux of a vector filed: .An a oriented surface S having attached in each of its points a normal vector to the surface the flux of the vector is defined as: .
The circulation of a vector field: Let be a vector field and and L be a smooth closed curve. The line integral is refered to as the circulation of the vector field A over the closed curve L.
Open mechanical system: if the external forces acting on a mechanical system can not be neglected then the considered mechanical system is called open.
Closed mechanical system: if the external forces acting on a mechanical system can be neglected then the considered mechanical system is called closed.
Conservative forces: Let us consider a stationary field of forces. If the work done on a particle by the forces of the field, to move the particle between 2 points A and B depend only on the initial and final positions of the particle moved between the point A and B, then these forces are called conservative.
The moment of inertia of the rigid body with respect to a given rotation axis: Let us denote by the moment of inertia of a body with respect to rotation axis passing trough its centre of mass, Also, let us denote by I the moment of inertia of a body with respect to any parallel rotation axis not passing trough its centre of mass. If the mass of the body is m and a is the distance between the 2 axis then .
The proper time: is a time measured on a clock maninig together with the particle. It has the form
II. 1. Newton`s law of motion:
Newton`s first law of motion:”every material object remains at rest or in uniform motion in a straight line as long as the net force acting on him is zero.” Newton`s second law of motion: “the net force acting on a body is equal to its mass times its acceleration and has the same direction and sense as the acceleration vector”. net =m ;
Newton`s 3rd law of motion: “whenever a body exerts a force upon a second body, the second body exerts an equal and opposite force upon the first body”.
2. Relativity Principle is Classical Mechanics:
The law of mechanics are invariant relative to the inertial reference system, i.e. these laws remain unchanged upon transition from one inertial reference from to another.
3. Basic Postulates of the Special Theory if Relativity.
The specials theory of relativity s based on two postulates formulated by Einstein in 1905:
1.All laws of physics are invariant relative to the inertial reference systems.
2.Light propagates in a vacuum at a definite constant speed, c =300x108m/s ,relative to any inertial reference system, not depending on the state of motion of omitting body or of the observer.
4. Basic postulates of the general theory of relativity
The general theory of relativity so based on two postulates formulated by Einstein in 1915:
1. All laws of physics are invariant relative to all reference systems, whether accelerated or not.
2. At any space-time point, a gravitational field is equivalent to an accelerated frame of reference in the absence of gravitational effects.
5. Hamilton`s Principle (Principle of the Last Action):” A system moves between position qK (t1) and qK (t2) in such a way that the action S has the smallest possible value”.
6. Steiner`s Theorem
Let us denote by ICM the moment of inertia of a body with respect to a rotation axis passing through its centre of mass. Also, let us denote by I the moment of inertia of a body with respect to any parallel rotation axis not passing through its centre of mass. If the mass of the body is m and a is the distance between the 2 axes.
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