June 24, 2018 Sunday
Bedtime Story
Holonomic and Non-holonomic Constraints
For our story, it is important to know that
constraint can either be holonomic or non-holonomic.
Without getting too technical, let me
briefly state what is meant by holonomic constraint.
Once again, mathematics has to be
introduced to define the idea of holonomic constraint.
A holonomic constraint is such that it
satisfies the following function:
f(x1,
x2, x3,…,xN, t) = 0
This is to say that a holonomic constraint
depends only on the coordinates x and time t.
What makes it special is that such a
constraint does not depend on any derivative of time t such as velocity and
higher derivatives such as acceleration.
This can be interpreted as a holonomic
physical system being such whose constraints are only a function of scalars and
not vectors.
On the other hand, a non-holonomic is a
system whose constraints cannot be expressed in the above manner.
This is so because the final state of the
system depends on just the coordinates but the intermediate values of its
trajectory through the space.
Another way to understand the idea of
constraints in a mechanical system is through the concept of degrees of
freedom.
Any physical system is characterized by
degree of freedom that is an independent physical parameter which can formally
describe a physical system.
One can also understand the degree of
freedom as the minimum number of coordinates required to specify a
configuration.
A single particle on a flat plane with only
x and y axis would have two degrees of freedom since just two coordinates
are needed to specify its configuration.
Similarly, a single point particle in a
three-dimensional space would have three degrees of freedom since three
coordinates are needed to specify its configuration.
It can be any useful property of the system
that is independent of variables.
To elaborate a little bit on this subject
of degree of freedom, consider a gas particle.
The center of this particle has three
degrees of freedom as a location of a point-article requires three position
coordinates.
This would be its translational and a
geometrical representation of this point.
The degree of freedom in a three
dimensional pace can be further decomposed to rotation and vibrations.
A point particle will remain unchanged if
it rotates and so its degree of freedom with relation to rotation is zero.
We shall continue out story on the degrees
of freedom in the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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