In this research, we study the material point motion, in the field of a
homogeneous and unbounded, material rod. so we present the
Hamiltonian formalization of the problem and study the orbits
located in the plans perpendicular to the rod. We reve
al the
proprieties of symmetry of those orbits, and present the conditions
to its closure.
We also study the material point motion, in the field of a
homogeneous and bounded, material rod. We present the
Hamiltonian formalization of the problem, reveal the practicality of
the plan of symmetry, and we studied the motion in this plan. We
reveal the existence of unbounded or bounded planar orbits; some
of those are closed. We also reveal that when the angular velocity
isn't null, there are not orbits leading to a collision with the rod.
In this paper, we study the gravitational field generated by a
material straight line around itself. We show the simplicity of the
studied field, and we show its relation with the arc of half circle. We
discussed also the subject of attracting two
spacious straight lines,
and we show the absence of relation between the mutual force and
the distance.
Also we study the field generated by a ray, where we present the
different formulas for this field, and we show its geometrics
properties, and its relation to a circular arc sees through it.
Also studied the previous field lines, and we show that it are
parabolas, and we appear by different ways that the equivalent
surfaces are parabolic surfaces of revolution.
In this paper, we study the gravitational field generated by a
straight material segment around itself. At first we discuss the
calculation of the field, outside the support of the segment, and on
this support, then we discuss the self field. We a
lso study values of
this field in special points.
We also study the field generated by a set of segments,, where we
interest in the value of this field in the common special points, and show
the cases where this field is finite, or infinite. We provide a set of
properties concerning the components of this field.
We also discussed the concept of falling on the material segment, where
we define the particular type of motion which we call successive motion,
and we show its conditions. This motion really present a falling on the
material segment.
This paper discusses the escape velocity for a limited material
distribution in a gravity field. This requeres examining the Newton’s
law of gravitation , the gravitational field vector of a limited material
distribution in a specific point and po
tential function togother with
the potential energy.
In paper, have proved that potential energy vanished in infinity . This
requires also examining Hamilton’s function then we have found the
escape velocity of a material point from a sphere’s surface ,when the
motion of the material point is vertical , horizontal or oblique .
We found the escape velocity for a material point from a disk in the
vertical and oblique cases.
In paper, we also find out the escape velocity from a ring in both
vertical and oblique cases . It is appeared that the escape velocity
from the ring identifies with that we get from the sphere case.
