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Can someone explain in an intuitive way how...
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Can someone explain in an intuitive way how newtons laws tell you that a particles trajectory is determined for all future time? I.e. that if you specify a position at t=0, you know where that particles going forever?
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$\frac{1}{m} \sum \limits_i \int F_i\ dt^2 = x(t)$
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Second law: F = ma.

The first law is a special case where F = 0, meaning that a = 0. The third law doesn't matter if you are thinking about a single particle.

The second law says that if you know the force on a particle at all times, then you know the acceleration at all times. If you know the acceleration, then you know how much the velocity is changing. If you know the velocity, then you know how much the position is changing.

It's just a cascade of information.

That's it, really. So you need to know the original position and velocity, and the force at all times.
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Dude, the world doesn't work In such a deterministic way. That's why quantum mechanics was created.
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>>7644014
>[eqn]
>\frac{d^2}{dt^2}\left(\vec{x}(t)\right) = \frac{\vec{F}(\vec{x},t)}{m}
>[/eqn]
trying $: [math] \frac{d^2}{dt^2}\left(\vec{x}(t)\right) = \frac{\vec{F}(\vec{x},t)}{m}$
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>>7644111
...
$\frac{d^2}{dt^2}\left(\vec{x}(t)\right) = \frac{\vec{F}(\vec{x},t)}{m}$
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>>7644014
Let me try
[eqn]\frac{d^2}{dt^2}\left(\vec{x}(t)\right) = \frac{\vec{F}(\vec{x},t)}{m}[/eqn]
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>>7644412
I think you have to do like \$... [math] >>7643995 It's not determined by its position at t=0. The trajectory is a function of speed, acceleration and position. >inb4 quantum mechanics talking about Noowton here >> >>7644420 The problem is \vec{} I think [math] \vec{x}$
$\frac{d^2}{dt^2}\left( \mathbf{x}(t)\right) = \frac{\mathbf{F}(\mathbf{x},t)}{m}$
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>>7644038

>freshman liberal arts major who just watched his first Neal DeGrasse Tyson video detected
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>>7644014
Formulas on /sci/ parse weird, even when they work in the previewer.

Generally, the problem can be solved by just throwing whitespace between all the control characters, parentheses, braces, operators, etc.
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>>7644434
I ran into this problem myself not long ago. I have no idea what causes it, but it seems to go away if I just put spaces between everything.
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>>7644441
Math major tyvm