Saturday 22 June 2013

Rubik's Cube

Hey Friends
     I am working on Rubik's cube, to find out the mathematics behind that. Hope for a better result. Till July 29 I will be working on this. Hope you will enjoy this.

Tuesday 28 May 2013

PSEUDO SPECTRA

This is my new research topic. Pseudo spectra related to Linear algebra. I am starting My research On this topic from Today ie 28th May 2013. From today onwards all My findings will be shown in this blog. Hope you all enjoy it . Want your feedback.
you can contact in my email ID
"ashwin@iiserb.ac.in" or "ashwin951@gmail.com"



 Notes will get publish from tonight itself.
   Ak

Friday 24 August 2012

moments

Moment of force (often just moment) is the tendency of a force to twist or rotate an object; see the article torque for details. A moment is valued mathematically as the product of the force and the moment arm. The moment arm is the perpendicular distance from the point of rotation, to the line of action of the force. The moment may be thought of as a measure of the tendency of the force to cause rotation about an imaginary axis through a point.[1] (Note: In mechanical and civil engineering, "moment" and "torque" have different meanings, while in physics they are synonyms. See the discussion in the "torque" article, or the article couple (mechanics).)
Image A shows a moment at Point O, when the components are perpendicular to the Point O. Image B and Image C illustrate the components of a Moment at Point O, when the components are not perpendicular to point O.
The moment of a force can be calculated about any point and not just the points in which the line of action of the force is perpendicular. Image A shows the components, the force F, and the moment arm, x when they are perpendicular to one another. When the force is not perpendicular to the point of interest, such as Point O in Images B and C, the magnitude of the Moment, M of a vector F about the point O is
\mathbf{M_O} = \mathbf{r_{OF}} \times \mathbf{F}
where
\mathbf{r_{OF}} is the vector from point O to the position where quantity F is applied.
× represents the cross product of the vectors.[2]
Image C represents the vector components of the force in Image B. In order to determine the Moment, M of a vector F about the point O, when vector F is not perpendicular to point O, one must resolve the force F, into its horizontal and vertical components. The sum of the moments of the two components of F about the point O is :
M OF = F * sin (θ) * x + F * cos(θ) * 0
The moment arm to the vertical component of F is a distance x. The moment arm to the horizontal component of F does not exist. There is no rotational force about point O due to the horizontal component of F. Thus, the moment arm distance is zero, or 0.[1]
Thus M can be referred to as "the moment M with respect to the axis that goes through the point O, or simply "the moment M about point O". If O is the origin, or, informally, if the axis involved is clear from context, one often omits O and says simply moment, rather than moment about O. Therefore, the moment about point O is indeed the cross product,
\mathbf{M_O} = \mathbf{r_{OF}} \times \mathbf{F},
since the cross product = F * x sin (θ)[1]
When F is the force, the moment of force is the torque as defined above.
guysss read this.......and send your feed back at ashwin@iiserb.ac.in

Tuesday 10 July 2012

Jerk

In physics, jerk, also known as jolt (especially in British English), surge and lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, the second derivative of velocity, or the third derivative of position. Jerk is defined by any of the following equivalent expressions:



Jerk is a vector, and there is no generally used term to describe its scalar magnitude 

The SI units of jerk are metres per second cubed (metres per second per second per second, m/s3 or m·s−3). There is no universal agreement on the symbol for jerk, but j is commonly used. ȧ,Newton's notation for the derivative of acceleration, can also be used, especially when "surge" or "lurch" is used instead of "jerk" or "jolt".
If acceleration can be felt by a body as the force (hence pressure) exerted by the object bringing about the acceleration on the body, jerk can be felt as the change in this pressure. For example a passenger in an accelerating vehicle with zero jerk will feel a constant force from the seat on his or her body; whereas positive jerk will be felt as increasing force on the body, and negative jerk as decreasing force on the body.
Note also the existence of yank—the derivative of force with respect to time.
for details about jerk 
               applications of jerk and yank is so complicated. Publish later...!!!!!!!!

                                                                                                     A K Nambiar

Sunday 8 July 2012

my inspiration to creat this blog

My inspiring quotes.................

  1.  "Imagination is more important than knowledge."-Einstein 
  2. "In rivers, the water that you touch is the last of what has passed and the first of that which comes; so with present time." -Leonardo da Vinci
  3. "A person starts to live when he can live outside himself." -Einstein
  4. “You cannot teach a man anythi
  5. ng; you can only help him discover it in himself.” -Galileo
  6. “The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the Universe to do.” - Galileo
  7. "An investment in knowledge pays the best interest." -Benjamin Franklin
  8. "An American monkey, after getting drunk on brandy, would never touch it again, and thus is much wiser than most men."  -Charles Darwin
  9. "A true friend is one soul in two bodies." -Aristotle
  10. "He who is fixed to a star does not change his mind." -Leonardo da Vinci
  11. “If I have seen further than others, it is by standing upon the shoulders of giants.” -Isaac Newton

You can post your advise regarding this blogger. Your  advices are the best blessing for me..