After
Newton made his mathematical explanation of the entire natural phenomenon with
his fundamental three laws, all the scientists started to work out many
physical problems using that.
The
three laws of Newton were conceived to be an essential thing for every motion
and all the problems were tried to solve based on these.
But,
solving of the problems headed into a great many difficulties.
There
is no any single doubt about the applicability or pertinence of these three
laws.
Newton’s
three laws are always applicable but it is not always a useful one.
The
reason may be,
Newton’s
definitions starts with the definition of a concept called particles. It says
that, the motion of each particle follows from the net external force acting on
that particle.
But all the entities in nature are not a
single particle. They all are some system of particles with definite shape,
size, etc. Besides, all the forces will not act at a single particle, but
rather at a certain position of the system of particles.
So,
we need a new way or mechanism to deal with these kinds of problems. The reason
is because, if you try to apply Newton’s laws for each of these molecules, then
note that, there are some order of 10^23 molecules in a mole of substance.
Though
Newton’s laws are applicable here,
though
it is certain that it will give a correct answer,
it
cannot be used here since we know for sure that it will never be achieved
writing equations of motion for all these particles.
It
may look, this need somewhat satisfied by the introduction of center of mass
concept but not completely.
Centre
of mass concept is just a simplified version of Newton’s law, where the third
law is utilized completely, where all the internal forces are taken as action,
reaction pairs and canceled out from the equations of motion.
But
this doesn’t alter anything about the nature of the force. The force is again
somewhat regarded as acting on a single particle, which is too much different
from the real situation.
All
these problems need a general way to solve the system of particles without
considering the internal properties of the system.
Let
us say the system is just a shadow. We don’t know whether there are particles
inside it and we know just the forces acting on that system.
Thus,
there is a great need for the sake of simple explanation of mechanical system.
Looking
for a new idea with this condition, it is found that the idea is there already
in our Physics, i.e. Thermodynamics.
In
Thermodynamics, though Volume, Pressure and Temperature are the manifestation
of microscopic phenomena, we characterize the thermodynamic system just only
with the macroscopic variables.
It
is just the final external effect i.e. Effective motion in mechanics is significant.
There
is no any concern about “the way how the final external effect is achieved”.
As
a result, one thing is to be sure that, the new mechanism should involve a more
geometrical approach rather than the physical approach. And so, Mathematics
plays a more fundamental role in this mechanism.
Explaining
the system with this new approach started by introducing a new concept namely,
Constraints.
Correspondingly,
the concept of constraints led to some new other essential concepts such as,
degrees of freedom; generalized coordinates; configuration space, etc. All these things exhibit the greatness of
classical mechanics in other fields of Physics.
