The region in a program where a variable is known is called the scope of the variable. A variable which can be accessed from anywhere in the program is called a top-level or global scope. A variable defined in a local scope can only be accessible from that scope.

   # global scope
   x = 1
   # local scope
   function scopes()
       println(x) # x is a global scope and accessible
       y = 1.0    # y is local to the function scopes
   end

  julia> println(y)

  ERROR: UndefVarError: y not defined
  Stacktrace:
  [1] top-level scope at none:0

   # example on for, while, try or let blocks
   y = 3
   for i = 1:10 #for loop is similar to the while loop
       y = i + 3
       if y == 6 #local variable inside a for-scope
	   println("The value of local y: $(y)")
       end
   end

   # inaccessible global variables in for and while loops
   y = 3
   while y < 10 #while-loop
       y += 1
       if y == 5
	   println("The value of local y: $(y)")
       end
   end

    ## without let block in a for loop
    anon = Array{Any}(undef, 2)
    for i = 1:2
	anon[i] = () -> println(i)
	i += 1
    end
    # anon function is called in julia to get

    julia> anon[1]()
    2

    julia> anon[2]()
    3
    ## using let block for i values to stick
    anon = Array(Any)(undef, 2)
    for i = 1:2
	let i = i
	    anon[i] = () -> println(i)
	end
	i += 1
    end
    # anon function is called in julia to now get
    julia> anon[1]()
    1

    julia> anon[2]()
    2

   x = 9
   function funscope(n)
       x = 0 # x is in the local scope of the function
       for i = 1:n
	   local x # x is local to the for loop
	   x = i + 1
	   if (x == 7)
	       println("This is the local x in for: $x") #> 7
	   end
       end
       println("This is the local x in funscope: $x") #> 0
       global x = 15
   end

An inverted pendulum on a cart is as shown in the figure.

The system dynamics defined by Newton's second law of motion can be written as the following set of equations.

\begin{align} \ddot{p} &= \frac{\dot{\theta}^{2} m L \sin \theta-\frac{3}{4} m g \sin \theta \cos \theta+u}{M+m-\frac{3}{4} m \cos ^{2} \theta} \\ \ddot{\theta} &= \frac{\frac{3 g}{4 L}(M+m) \sin \theta-\frac{3 m}{4} \dot{\theta}^{2} \sin \theta \cos \theta-\frac{3}{4 L} u \cos \theta}{M+m-\frac{3}{4} m \cos ^{2} \theta} \end{align}

Given the dynamics, the state vector can be chosen to be the positions & velocities.

\(\mathbf{x}=\left[ \begin{array}{c}{\theta} \\ {\dot{\theta}} \\ {p} \\ {\dot{p}}\end{array}\right]=\left[ \begin{array}{c}{x_{1}} \\ {x_{2}} \\ {x_{3}} \\ {x_{4}}\end{array}\right]\)

The nonlinear state equations as functions of the states and inputs

\begin{aligned} \dot{\mathbf{x}} &=\mathbf{f}(\mathbf{x}, u) \\ y &=g(\mathbf{x}, u) \end{aligned}

can be written as,

\begin{align} \mathbf{\dot{x}} = \left[ \begin{array}{c}\dot{\theta} \\ {\ddot{\theta}} \\ \dot{p} \\ {\ddot{p}}\end{array}\right] &= \left[ \begin{array}{c}{x_{2}} \\ \frac{\frac{3 g}{4 L}(M+m) \sin x_{1}-\frac{3 m}{4} \sin x_{1} \cos x_{1} \cdot x_{2}^{2}-\frac{3}{4 L} \cos x_{1} \cdot u}{M+m-\frac{3}{4} m \cos ^{2} x_{1}} \\ x_{4} \\ \frac{m L \sin x_{1} \cdot x_{2}^{2}-\frac{3}{4} m g \sin x_{1} \cos x_{1}+u}{M+m-\frac{3}{4} m \cos ^{2} x_{1}} \end{array}\right] \\ y = p &= x_{3} \end{align}

The state equations above are description of a nonlinear system due to the sine and cosine values. The stationary state is selected as \(\mathbf{x}_{0}=\left[ \begin{array}{llll}{0} & {0} & {0} & {0}\end{array}\right]^{T}\) and these nonlinearities can be linearly approximated by assuming that \(\sin \theta \cong \theta, \cos \theta \cong 1\) and \(\dot{\theta}^{2} \cong 0\)

Substituting these values in the state equations gives,

\begin{align} \dot{x}_{2} &= \ddot{\theta} \cong \frac{\frac{3 g}{4 L}(M+m) \theta-\frac{3}{4 L} u}{M+\frac{m}{4}} \\ \dot{x}_{4} &= \ddot{p} \cong \frac{-\frac{3}{4} m g \theta+u}{M+\frac{m}{4}} \end{align}

At the stationary point calculating the Jacobian matrix, the partial derivatives of the state equations with respect to the states and inputs, will give the linearized state equation where \(\Delta\) variables are perturbation from the stationary point.

\begin{align} \dot{\Delta x} &= \left[ \begin{array}{cccc} 0 & 1 & 0 & 0 \\ \frac{3 g(M+m)}{\left(M+\frac{m}{4}\right) 4 L} & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \frac{-\frac{3}{4} m g}{M+\frac{m}{4}} & 0 & 0 & 0 \end{array} \right] \Delta \mathbf{x}+ \left[ \begin{array}{c} 0 \\ \frac{-\frac{3}{4 L}}{M + \frac{m}{4}} \\ 0 \\ {\frac{1}{M+\frac{m}{4}}} \end{array}\right] \Delta \mathbf{u} \\ \Delta y &= \left[ \begin{array}{llll}{0} & {0} & {1} & {0}\end{array}\right] \Delta \mathbf{x} \end{align}

This has been one of the best novels I've read in a while. The main protagonist Anton Hoffmiller, an army officer, is also the narrator of the plot in this book. Reading through the raw emotions of a person falling in contempt with his compassion and finally it turning into a smoke of guilt is what burns through this book. I've thoroughly enjoyed the read and have learnt about how people in a different time felt & thought; the human things they had stuggled within societies and those that we still wrangle with today.

Reading this book has given an insight into my friends' and neighbours' lives, the evolving nature of their environment which was well hidden from the experiences I've had throughout my childhood and adult life until now. Thanks to Sujatha Gidla and her beautifully presented book 'Ants Among Elephants', we can see the whole picture and not the contorted version of truth that was passed on amongst certain castes with a clear intent to undermine the views of a major set of the society we are living with. The events presented in the book reminded me of my grandfather's stories, who worked as a lecturer in various schools, which would end abrubtly leaving the people in it stranded within the listener's imagination without any moral at the end to them as I'd been used to in the various children's storybooks but the stories were all the more captivating. The author too kept me in the web of events that is her family's life beautifully knit one after another and it is hard to keep this book away for too long while reading it.

I'd always wondered what the beautiful caligraphy on the walls spelling out the letters 'CPI', 'SFI' in the streets of Hyderabad with distinct flags next to them stood for. They had been political organisations was all that was known and these intricately painted walls were their passion to their organisations. It seemed to my naive youger self that it was a waste to have so many political parties actively competing for the same positions; as almost all of the contests were won by the major political parties. But now it is clear to me and to whomsoever would read this book that the major political parties have been inadequate in solving the problems and have not only created but also perpetuated a few more.

Ants Among Elephants has been a gut wrenching read and there were several instances where it has been an answer to curious loose-ends that lingered as distinct memories but more so painful is to read through the experiences of people. This book and its author have been a compass to my values and will be to the young of India as it describes the true history of the country.

This year started off in a hope to read more books than I'd ever read in one. Since not being as fast a reader as my friends, an acheivable but a good target was to complete twelve books in 12 months.

Two more months remain for this year and three books to be completed. I'm looking forward to raising the bar a bit higher the next year and onwards post about the book read as they are completed.

Now is october(month 10.) already and these are the books that I've read so far:

This blog is setup using emacs, orgmode(part of emacs), anaconda – for virtual environment, nikola and github – for hosting your blog. This post will take you through the steps that I've followed in order to get this blog that you are currently reading up and running from an Ubuntu machine. This is part of an exercise to write more frequently on this blog inspired by Sacha's guide on how-to.

Firstly, we can find instructions to install Emacs and orgmode on their respective webpages.

   # Create a virtual environment using '-n <name>', here blog.
   $ conda create -n blog python=3

   # Activate the conda virtual environment 'blog' created earlier
   $ source activate blog
   # Install nikola using pip
   (blog)$ pip install --upgrade pip 'Nikola[extras]'