The main objective of this course is to introduce students of physics to the 'modern' formalism of classical (or Newtonian) mechanics, especially Lagrangian and Hamiltonian mechanics. An important part of the course will focus on introducing the variational methods and principles in mechanics, or m...
Jawad Cheayto
Newtonianmechanics are founded upon
the three Newton's
laws Audio 1
Newton's Laws
Firstlaw lawofinertia
There exists aframe in whichan
ofreference
isolated particleon which no externalforces
is applied stays at rest or keeps a uniform
rectilinear motion Éo a O a test
Note Areferenceframe in whichthefirst Newton's law
is valid is called inertial or Galilean frame
repitition
The this is stated mightsound like a
way tautology
Amore transparent wayof expressingthings would
be like
There existinertialframes
Audio2
Second Newton's law fundamental law
of dynamics
Theforce Éapplied to a materialpoint is equal
tothe product of its mass'm its acceleration a i
by
where at di
É met m
dj y at
ELI is of
, Observethat mast in classicalmechanics
So
dip where mo
at
Md's in daff daniil DE
dt dt
Thirdlaw Principleofaction4reaction Audio3
Theforce Is exerted by a particle 1 on particle2
isthe opposite
of
the
force exerted
by
theparide 1
on particle 2
Fas
7
Faz 2
o y
I 2
The three Newton'slaws are valid in inertialreference frame or
Galileanreferenceframe
AGalileanreferenceframe is aframe
at rest or having a uniformrectilinearmotion
Instead 2 arbitrary Galileanframes are either at restrelative to each
other oroneis
moving
with a constant velocity with respect tothe other
,for practical proposes a system of reference
Audio4
having small acceleration can be a good approximation
to an initialframe depending onthe problemconsidered
I For almost all
of
terrestrial problems a frame
of
reference fixed to a point on the surface of
the Earth
is a good approximation to an initialframesince
its acceleration around the axis of rotationof the
Earth is
of the order a o 034m15
2
Earth
reattached rigidly
1 to the axis of earth
z
x
2 for the studyofthemotion of the moon andartificial
satellites around the Earth we can use aframe whose
attached to the center the Earthand
origin is of moving
withit around the sun but not rotating around theaxis
ofthe Earth i The axis of this
frame have fixed
directions with respect to fixed stars Tk acceleration
of such frame is
of
the order a 6 103m15
, aoaaaiaaa.B.a.gg aoaaaia.o.am.am
atdagYfgppG
son
3 for thestudy ofthe motion of planets in the solar
system around
the sun we choose a frame whose
origin
is attached to the center
of mass of
the solar
system
which is practically the center the sun This
of frame
moves with the sun around the centerofthegalaxy
but its axis keepfixeddirections withrespect tofixed
2
this system is
stars Tk acceleration
of oforder as 3 10 15
our
galaxy
thegg.traat r
son od
solar
system
Audio5
Remark In an inertialframe the orientation andposition
isolated
system are equivalent
of an
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