School is going well, teaching "ASEN3128" at CU.

I'm writing this mostly for myself, so apologies if you're a reader and find this post boring. Somehow writing for publication makes this seem easier than just scribbling it down somewhere. Or maybe it's because it's so easy, I don't know.

Anyway, I am developing a...

It has several parts: First there's a review. This is just repeating what happened in the last lecture.

Second, a hook. To get them interested, calmed down, and foreshadowing the day's topic. Sometimes I use the hook as part of the summary so I guess I'm not rigorous about it pertaining to the new material.

Next of course is the body of the lecture. There are lots of sub-topics here. Last is the crescendo. It's supposed to be a surprise opening up a new area to think about. Some examples will clarify.

Lecture 1: Hook: picture of an airplane window: nothing seems to be happening. It is as if there is no motion, and this is balance, this is trim. Course outline. Discuss longitudinal trim, CMa and CMq and CMde. The many dichotomies of this course: trim vs perturbations. s vs z, Laplace vs integration, TF vs SS, Block Diagram Algebra vs Matrix notation, roots vs bode, decay vs oscillatory, Euler vs Quat. Numerical simulation of low pass, and hints of chaos. Of course these were discrete simulations, F(z), but we didn't touch on that much.

Lecture 2: The review was the stability derivatives & dichotomies. Hook was the chaos simulation, showing how its nonlinearity makes it insoluble. Direction Cosines, and the network diagram method of deriving them instantly. Crescendo: Quaternion is that one vector which is unchanged by a DCM. Stability Axes

Lecture 3: Hook = Close your eyes and imagine you're on a beach, running for the frisbee. Invert the scene with a rolling dive. Here the hook was actually part of the review of DCM. Meat was roll subsidence and stability axes. Stability derivatives with units of 1/t, and normalizations to get there. Introduction to block diagrams. Introduction to [A]x = sx as an eigenvalue problem: find eigenvalues of [sI-A]=0

Lecture 4: Hook = throwing tennis ball. Experts just catch it. Experts can guess the right answer. We will guess the answer is exp(at) or exp(st). Metapor for a match, which is a useful tool that separates us from the animals. We need to be good match (Laplace method) users. Body of the class to discuss roll subsidence from two perspectives: Laplace method (d/dt --> s, crack the poly, then "just know" the pattern from roots to dynamics) and formal integration of the differential equation (much harder) required an integrating factor, integration by parts, homogeneous and particular solutions. Showed the root::dynamics correlations, speed for real roots, frequency & damping for imag ones. The crescendo was discussing rolling a tennis ball across the floor: it would go forever. That was a *very* slow/large/long time constant, zero in fact. 1/(s+a) with a going to 0. We did NOT get to Laplace Transforms, which is another method, requiring convolution and inverse-Laplace{F(s)}. We did not get into numerical simulation but we certainly will.

Lecture 5: Bigger review 'since quiz next time. Homework review: what does a matrix [Cib] do to an eigenvector? Nothning; lambda was 1. How about a matrix [A] (multiply, to attenuate, but not to change). The bulk of the lecture will be on stability derivatives, and more trim, lateral this time.

Lecture 6: Quiz.

Lecture 7: Laplace transforms: computing some. 1, t, exp(at) sin?, L{f(t)}Using Lspecifically convolution of impulse response with step. LPF (something you might do explicitly in code)

Lecture 8: Pitch Short Period. Weathervane without a wing. Surprise, q integrates to give alpha (as well as theta). Without a wing that's clear. It's a demonstration of Euler's equation, too. Full EOM (pitch)

Lecture 9: Rocket is not am inverted pendulum. Aircraft is not a pendulum. The force does not produce a feedback that changes the orientation & hence the force, as it does in the pendulum.

I need to do this for office hours a little bit too, because there's the one-on-one Q&A which is ineffective, but maybe necessary if students are afraid / embarrassed. Just general Q&A about the homework is a good forum to explore confusions, but I'd like it if that were classroom-wide

I'm writing this mostly for myself, so apologies if you're a reader and find this post boring. Somehow writing for publication makes this seem easier than just scribbling it down somewhere. Or maybe it's because it's so easy, I don't know.

Anyway, I am developing a...

**Lecture Style or Pattern**It has several parts: First there's a review. This is just repeating what happened in the last lecture.

Second, a hook. To get them interested, calmed down, and foreshadowing the day's topic. Sometimes I use the hook as part of the summary so I guess I'm not rigorous about it pertaining to the new material.

Next of course is the body of the lecture. There are lots of sub-topics here. Last is the crescendo. It's supposed to be a surprise opening up a new area to think about. Some examples will clarify.

Lecture 1: Hook: picture of an airplane window: nothing seems to be happening. It is as if there is no motion, and this is balance, this is trim. Course outline. Discuss longitudinal trim, CMa and CMq and CMde. The many dichotomies of this course: trim vs perturbations. s vs z, Laplace vs integration, TF vs SS, Block Diagram Algebra vs Matrix notation, roots vs bode, decay vs oscillatory, Euler vs Quat. Numerical simulation of low pass, and hints of chaos. Of course these were discrete simulations, F(z), but we didn't touch on that much.

Lecture 2: The review was the stability derivatives & dichotomies. Hook was the chaos simulation, showing how its nonlinearity makes it insoluble. Direction Cosines, and the network diagram method of deriving them instantly. Crescendo: Quaternion is that one vector which is unchanged by a DCM. Stability Axes

Lecture 3: Hook = Close your eyes and imagine you're on a beach, running for the frisbee. Invert the scene with a rolling dive. Here the hook was actually part of the review of DCM. Meat was roll subsidence and stability axes. Stability derivatives with units of 1/t, and normalizations to get there. Introduction to block diagrams. Introduction to [A]x = sx as an eigenvalue problem: find eigenvalues of [sI-A]=0

Lecture 4: Hook = throwing tennis ball. Experts just catch it. Experts can guess the right answer. We will guess the answer is exp(at) or exp(st). Metapor for a match, which is a useful tool that separates us from the animals. We need to be good match (Laplace method) users. Body of the class to discuss roll subsidence from two perspectives: Laplace method (d/dt --> s, crack the poly, then "just know" the pattern from roots to dynamics) and formal integration of the differential equation (much harder) required an integrating factor, integration by parts, homogeneous and particular solutions. Showed the root::dynamics correlations, speed for real roots, frequency & damping for imag ones. The crescendo was discussing rolling a tennis ball across the floor: it would go forever. That was a *very* slow/large/long time constant, zero in fact. 1/(s+a) with a going to 0. We did NOT get to Laplace Transforms, which is another method, requiring convolution and inverse-Laplace{F(s)}. We did not get into numerical simulation but we certainly will.

Lecture 5: Bigger review 'since quiz next time. Homework review: what does a matrix [Cib] do to an eigenvector? Nothning; lambda was 1. How about a matrix [A] (multiply, to attenuate, but not to change). The bulk of the lecture will be on stability derivatives, and more trim, lateral this time.

Lecture 6: Quiz.

Lecture 7: Laplace transforms: computing some. 1, t, exp(at) sin?, L{f(t)}Using Lspecifically convolution of impulse response with step. LPF (something you might do explicitly in code)

Lecture 8: Pitch Short Period. Weathervane without a wing. Surprise, q integrates to give alpha (as well as theta). Without a wing that's clear. It's a demonstration of Euler's equation, too. Full EOM (pitch)

Lecture 9: Rocket is not am inverted pendulum. Aircraft is not a pendulum. The force does not produce a feedback that changes the orientation & hence the force, as it does in the pendulum.

I need to do this for office hours a little bit too, because there's the one-on-one Q&A which is ineffective, but maybe necessary if students are afraid / embarrassed. Just general Q&A about the homework is a good forum to explore confusions, but I'd like it if that were classroom-wide

## No comments:

## Post a Comment