@@ -8,7 +8,7 @@ One first step is building an ODE simulation of a pendulum, and rendering that.
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@@ -8,7 +8,7 @@ One first step is building an ODE simulation of a pendulum, and rendering that.
OK, to start, the pendulum itself can be modelled with:
OK, to start, the pendulum itself can be modelled with:
$$\ddot{\theta} = \frac{g}{l}\sin \theta $$
$` \ddot{\theta} = \frac{g}{l}\sin \theta `$
Where $\theta$ is the angle of the pendulum, $g$ is gravity, and $l$ is the length of the pendulum.
Where $\theta$ is the angle of the pendulum, $g$ is gravity, and $l$ is the length of the pendulum.
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@@ -44,7 +44,7 @@ to continue,
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@@ -44,7 +44,7 @@ to continue,
Then I'll be satisfied with code. And I'll want to see about some learning! Looking at phase plots, and starting to think about control. My first useful output from the simulation, as well, will be knowledge of whether / not I can reasonably expect my current physical axis (w/ speed, accel limits known to me) will be *enough* to spin up a pendulum of some length.
Then I'll be satisfied with code. And I'll want to see about some learning! Looking at phase plots, and starting to think about control. My first useful output from the simulation, as well, will be knowledge of whether / not I can reasonably expect my current physical axis (w/ speed, accel limits known to me) will be *enough* to spin up a pendulum of some length.
I'd also love to know / understand more about where-all / how friction values relate to damping terms. For the stepper, I'll completely simulate the damping, at the motor, but for the pendulum, I'd like to know what order magnitude to expect.
I'd also love to know / understand more about where-all / how friction values relate to damping terms. For the stepper, I'll completely simulate the damping, at the motor, but for the pendulum, I'd like to know what order magnitude to expect.