Of dissipative forces and the totality of motion

The idea of totality of motion is a rather interesting and would come to human minds as common sense. It is however, very different. This would be my concern in my development of mechanics with arc length as parameter. Let me share this idea I have, that has been in my mind for some time now. Consider a dissipative force. It is, of course, always act opposite of the direction of motion. Now try to integrate the force through the region where it retraces its path. Because we have said the force acts opposite the direction of motion, the sign must change whenever the direction changes. Thus the integral that we are doing is separated into two parts, one with positive sign and the other negative. That is

F = - sgn(v) F(q)

or

F = - sgn(v)F(dq/dt)

The work done by

W = - (int( sgn(v) F(q)dq)

and

W = - (int(sgn(v)F(dq/dt)d(dq/dt)dt).

The presence of sgn(v) implies the separated parts of the integration in accordance to sign. Now I present this idea of mine, which I am not sure of its truth. If we parametrized this function F with the arc length, s , and put restriction such that W(a) > W(b) for a>b, we will have a irreversible work function and we may replace the integral mentioned with a single integral. Furthermore, the bijectivity of the arc length function tells us that F may be a function of s ( F that is function of ds/dt may be mapped as F(s)).

Now comes the issue of the totality of motion. If the motion can be determined by its initial conditions, that is q = f(t) and dq/dt = f'(t) (which implies s = g(t) and s'= g'(t)), can the force be parametrized as above? Can it be related to such deterministic mapping? What happens if this force is seen from the quantum mechanical perspective? Can we assume the solution exist, and work with the known form of the solution, not the equation itself? These are questions that remain for me to answer, which to some degree, philosophical. I do hope readers will enlight me and provide insights that supports or reject my proposition.

Of myself, ambition and reality.

I was intrigued by the idea of blogging some time ago, but only now I start . I am not sure myself whether anything led me to this, but I don't think any justification is needed. However, I realized I had ideas, tonnes of it, and it would be nice to share and be corrected. As some of my friends might know, I am rather a one sided person. A science person, a person that loved physics and perhaps happy to spend a lifetime to understand the nature and creation of Allah. I am in a different class, not all rounded, far from all those geniuses, scholars and top scorers. This blog would focus on, but certainly not limited to, discussions on developments of physics, physical reality, axiomatic problems and maybe a few philosophical thoughts.
Having laid down some introduction of myself, it is rather helpful to say something about my personal views on life. Recently, I was struck with realizations of reality, what is it that I want to achieve. What I want to do in my life. I looked back, thought about the past and present. During times of schooling, my peers and I had this obsession of studying for the sake of good results in examinations. Or rather memorizing for examinations. We didn't set out to understand the world, to get most from it, to know what Allah created for us. Instead, we memorized and practiced how to answer questions, for our aim was good results in examinations and scholarships etc. Then, when it mattered, I failed. Putting me far behind everyone in terms of achievements. It threw me into terrible times, but of that we shall not discuss. It suffices to say because of that, I had reexamined the reality, the meaning of achievement, the meaning of it all. I was lucky to be given a new hobby, that was appreciating physics. At times where my understanding of success was still worldly, I hoped to study physics as means to have success, to have the chance to enjoy the taste of victory and to get away from the agony of defeat. When in course of my study, I learned that the world is very mathematical, everything falls into order as described in the Koran. The more I learned, the more I see the reality of nature. The more of things described in the Koran. It brought me pleasures of discoveries (especially after starting to inquire the nature myself) and also made me feel small, for the realizations of the wonders and the beauty of nature as created by Allah. It was enough to persuade me to devote my time, as a slave of Allah and temporary occupant of the universe, understanding the nature, as it was encouraged by Islam. However, until recently, I concentrated entirely on this pursuit, but with some feeling for worldly recognition. It was a poem by the magnificent astronomer, mathematician and poet Omar Khayyam that diverted me to avoid those wanting of worldly ambitions. These phrase changed me and made me look myself at the time when I was at high school as idiotic and naive;
"Both thou and I are born alike;
Though some may sink and some may soar,
We all are earth, and nothing more."
This phrase made me think, as what Omar Khayyam thought, of the futility of life. The nothingness of it. This world has nothing beneficial, except following the Koran and Sunnah. We shall die and return to Allah one day. I was ashamed and humiliated by myself, for all my stupidity and worldly ambitions. From then on, I know what exactly I suppose to do with this life given to me.
Summing up, I gave some views and experiences that defined myself as a person. I realized that I am not a good person, especially a Muslim, and I will try to be one (but I know it could never be done, as no one would ever be perfect). My views may be different and some might criticize, but notice everything, all the criticism, are addressed to myself. Because you arrived to this sentence, with due modesty I thank you for your attention. I welcome any constructive comments and of course, any corrections and criticism.