Linearization PROOF | Nonlinear Dynamics (Part 3 extra)

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Physics
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11th - 12th Grade
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Hard
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7 questions
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1.
OPEN ENDED QUESTION
3 mins • 1 pt
What are the fixed points of the system of differential equations discussed in the video?
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2.
OPEN ENDED QUESTION
3 mins • 1 pt
Explain the process of performing a Taylor series expansion around a fixed point.
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3.
OPEN ENDED QUESTION
3 mins • 1 pt
What is the significance of neglecting higher order nonlinear terms in linearization?
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4.
OPEN ENDED QUESTION
3 mins • 1 pt
What coordinate transformation is suggested to solve the issue with the fixed points?
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5.
OPEN ENDED QUESTION
3 mins • 1 pt
Describe how the linearized equation of motion is derived from the original equations.
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6.
OPEN ENDED QUESTION
3 mins • 1 pt
What are the limitations of linearization theory as mentioned in the video?
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7.
OPEN ENDED QUESTION
3 mins • 1 pt
How does the trace and determinant of the matrix A affect the reliability of linearization?
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