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--- frameworks:newtonian_formalism [2018/04/12 16:15]
bogumilvidovic [Intuitive]
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-====== Newtonian Framework======
-<tabbox Intuitive>
-In the Newtonian formalism, we describe what happens in a system in terms of trajectories. For example, the path of a point-like object could look as follows:
-{{ :particletraj2.png?nolink&600 |}}
-<tabbox Concrete>
-The equations and the framework of classical mechanics were deduced historically from experiments. This worked pretty good but is highly unsatisfactory from a theoretical point of view. Newton proposed his [[equations:newtons_second_law|second law]]
-\begin{equation} \label{newtonssecond}  \tag{1} F = m \frac{d²}{dt²}q =m \ddot q,  \end{equation}
-where $m$ is the mass, $\ddot q$ the acceleration and $F$ the force that acts on the object in question.
-To describe some object we simply have to deduce equations for the forces $F$ that act on the object from experiments and put them on the left-hand side of the equation. This yields a differential equation, which we must solve for $q=q(t)$.
-The solution is called the trajectory of the object and describes the position of the object for every moment in time. This is one framework for classical mechanics and it‘s useful for many, many things.
-Every student of physics has to solve Newton's second law for many different situations.
-----
-**First law:**
-If the forces acting on an object are balanced, i.e. the total force is zero $\vec F=0$, the velocity of the object will remain constant: $\vec v=\text{const}$. So when the velocity is zero, it will remain zero. If the velocity has some other value it will keep it.
-<diagram>
-||||| AA|| |AA=Forces are balanced $ \vec F=0$
-||||||!@4|||||||
-|||||BB||||||BB=$ \vec a=0$
-||||,@4| -|^|- |.@4 | | | |
-||| AA||BB |AA=Object at rest: $\vec v=0$|BB=Object in motion $ \vec v\neq 0$
-||||!@4||||!@4|||
-||| AA||BB |AA=Object stays at rest: $\vec v=0$|BB=Object remains in motion $ \vec v \neq 0$; same $ \vec v$.
-</diagram>
-**Second law:**
-$$ \vec F = m \vec a$$
-<diagram>
-||||| AA|| |AA=Forces are unbalanced $ \vec F\neq 0$
-||||||!@4|||||||
-|||||BB||||||BB=$ \vec a \neq 0$
-||||,@4| -|^|- |.@4 | | | |
-||| AA||BB |AA=acceleration $\vec a$ depends directly on the net-force $\vec F$ that acts on the object|BB=acceleration $\vec a$ depends inversly on the mass $m$ of the object
-</diagram>
-<tabbox Abstract>
-<note tip>
-The motto in this section is: //the higher the level of abstraction, the better//.
-</note>
-<tabbox Why is it interesting?>
-The Newtonian formalism is a framework that allows us to predict how a system will evolve.
-It is still one of the most popular ways to describe what happens in a physical system. In contrast to the alternative [[frameworks:schroedinger_framework|Schrödinger framework]] it is much easier to understand what is going on, since only concepts that are directly familiar to high-school students are used.
-----
-<blockquote>
-Nature and Nature’s laws lay hid in night:
-God said, "Let Newton be!" and all was light. <cite>Alexander Pope</cite></blockquote>
-</tabbox>

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