31 lines
970 B
Markdown
31 lines
970 B
Markdown
---
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title: Frameworks and Review
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allDay: false
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startTime: 12:30
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endTime: 14:30
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date: 2024-09-09
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completed: null
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type: single
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---
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# Introduction
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Where do nonlinearities come from?
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Well, a couple of places...
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1. Geometric nonlinearities (pendulum)
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2. External fields
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3. Material properties
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So we're stuck with them. But how do we deal with noninearities?
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## A nonlinear equation
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$$ \dot{x} = \frac{dx}{dt} = 1-2\cos x$$
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How do you solve this? You can't use Laplace, you can't separate...
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*insert very long expression that Bajaj wrote.*
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Getting an analytical solution can be a PITA to obtain. For this reason:
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**The general case is that nonlinear equations are unsolvable.**
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This doesn't mean we can't learn things. We can describe these systems *qualitatively*.
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Really our options come down to:
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- Solve exactly (Not likely to happen)
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- Solve numerically
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- Analyze qualitatively (~geometrically)
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- Solve an approximation to the problem
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We mix and match these approaches. |