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Christopher Scott Vaughen
Registrace 12. 09. 2007
Mathematics related videos
The 3-Body Problem: An Introduction by Alexis Andrulonis
An introduction to the math and physics of the 3-body problem. Includes history, animations and a discussion of the special case of the circular restricted 3-body problem.
This presentation was part of an independent study course on mathematical modeling and scientific computing at Montgomery County Community College in Spring 2024.
Music used for the animations:
* Event Horizon by Lunar Years at Bensound.com, license code OXNMA1FTOL8TNGTW
* Ophelia by Roo Walker at Uppbeat.com
This presentation was part of an independent study course on mathematical modeling and scientific computing at Montgomery County Community College in Spring 2024.
Music used for the animations:
* Event Horizon by Lunar Years at Bensound.com, license code OXNMA1FTOL8TNGTW
* Ophelia by Roo Walker at Uppbeat.com
zhlédnutí: 152
Video
The Three-Body Problem: Introduction and Simulation
zhlédnutí 14KPřed 8 měsíci
An introduction to the three-body problem with an explanation of the math and physics using a simulation written in python. Includes examples of stable solutions. Music from #Uppbeat (free for Creators!): uppbeat.io/t/revo/universal License code: H8LISAQDTUVM057L Thanks to Dr. Rhett Allain for the introduction to VPython and Trinket.io and his video on the 3-body problem here: czcams.com/video/...
The Vis-Viva Lab - With Real Life Data!!
zhlédnutí 244Před rokem
A study of conservation of energy and angular momentum for real-life celestial objects, using data downloaded from NASA's HORIZON orbit tracking system. Examples include the International Space Station, the near-Earth asteroid Apophis, the Tesla Roadster carrying Starman, and the interstellar object Oumuamua.
The Vis-Viva Lab
zhlédnutí 287Před rokem
We confirm conservation of energy and angular momentum using the computer game Kerbal Space Program as a virtual lab. Learn more at sites.google.com/view/kspmath Music credits: Kerbal Space Program soundtrack, and, from Free Music Archive: HoliznaCCO, John Bartmann, Lobo Loco, lost-radio, Sergey Cheremisinov
Channel Trailer
zhlédnutí 376Před rokem
Clips from previous videos: first video posted September 11th, 2012, now 10 years ago!
Modeling the Flight Dynamics of Gliders
zhlédnutí 1,8KPřed 2 lety
We derive a mathematical model for the longitudinal oscillation of a glider (also called phugoid motion) using a system of nonlinear differential equations (Zhukovsky's equations) and solve those equations with Mathematica. We then compare the mathematical model with three flight simulators: Geo-FS, Kerbal Space Program, and Microsoft Flight Simulator.
Modeling a Pandemic with Excel
zhlédnutí 1,5KPřed 2 lety
We develop a discrete-time model of a pandemic and implement the model in Excel. We then compare the model with the standard SIR model and with a standard Markov model. Thanks to: Professor Jacob Glower for his video: czcams.com/video/dN9msZSlstg/video.html Also, thanks to the following for their videos on modeling a pandemic: 3Blue1Brown (for the pandemic simulation): czcams.com/video/gxAaO2rs...
Modeling the flight of a glider with Mathematica and KSP
zhlédnutí 1,5KPřed 2 lety
We derive a set of differential equations to model the flight of a glider, find solutions to these equations with Mathematica, and then compare the solutions with flights in the computer game Kerbal Space Program. We also find expressions for both terminal and trim velocity by considering particular solutions to the equations. The equations derived here are sometimes referred to as Lanchester's...
The four card problem
zhlédnutí 1,9KPřed 2 lety
The four card problem is an interesting analysis of both the logic of conditional statements and also psychology.
Optimal Rocket Staging with Lagrange Multipliers
zhlédnutí 1,8KPřed 2 lety
An application of Lagrange multipliers (from multi-variable calculus) to the problem of finding optimal mass for each stage of a multi-stage rocket. We look at an introduction to Lagrange multipliers, a derivation of formulas for finding optimal mass, and compare theoretical results with the Saturn V, Falcon 9, Starship and an example in Kerbal Space Program. Additional written explanation and ...
Calculate True and Magnetic Heading
zhlédnutí 983Před 2 lety
We calculate the true and magnetic heading and illustrate an example in Microsoft Flight Simulator 2020 with a flight from Wings Field in Blue Bell, PA to the Montgomery County Community College Central and West Campus and land at Heritage Field in Pottstown, PA.
The Prague Astronomical Clock
zhlédnutí 7KPřed 2 lety
How to read the Prague Astronomical Clock and some mathematics behind the clock's design. Website used through video is www.orloj.eu/en/home1.htm Astronomy simulations and tutorials used in this video are from stellarium.org and astro.unl.edu Videos referenced at beginning are here: Honest Guide: czcams.com/video/43KRqMoVM1I/video.html The Masked Guide: czcams.com/video/6k8T1YX5n8Q/video.html A...
Teaching Math & Physics with Kerbal Space Program
zhlédnutí 2,7KPřed 3 lety
Thank you to the NASA Pennsylvania Space Grant Consortium, Montgomery County Community College, Private Division, Marco, Jay, Cody, Nick and Scott Manley for making this possible - it was a fantastic learning experience for my students and for me as well. Thank you to ShadowZone for the Cybertruck, Janus92 (on KerbalX.com) for the Starship re-creation, and Jett Quasar for the Stryder which beca...
Starship Moon Landing, Part 2: Mathematics of Navigation
zhlédnutí 675Před 3 lety
A calculus based derivation of rhumb line heading and distance formulas for navigation on any spherical planet or moon. Part 2 in the Starship Moon Landing series illustrating mathematics in aerospace with Kerbal Space Program.
MAT 140 Lesson 12: Markov Model of a Pandemic
zhlédnutí 553Před 3 lety
Using a Markov process to model a pandemic. Introducing matrix multiplication, the Markov process and an implementation in Excel. Here is Excel file: drive.google.com/file/d/1AqP4UPv8hPNkT_mwDvL4XJdG7VBuaIz7/view?usp=sharing
Exponential Rates of Consumption and Production of Finite Resources
zhlédnutí 255Před 3 lety
Exponential Rates of Consumption and Production of Finite Resources
MAT199 NASA KSP Math & Physics Lab Fall 2020
zhlédnutí 922Před 3 lety
MAT199 NASA KSP Math & Physics Lab Fall 2020
Orbit Inclination, Launch Azimuth and Latitude
zhlédnutí 12KPřed 3 lety
Orbit Inclination, Launch Azimuth and Latitude
MAT 125 Lesson 16: Intro to Graph Theory, Part 2
zhlédnutí 641Před 4 lety
MAT 125 Lesson 16: Intro to Graph Theory, Part 2
MAT 125 Lesson 16: Intro to Graph Theory, Part 1
zhlédnutí 814Před 4 lety
MAT 125 Lesson 16: Intro to Graph Theory, Part 1
Line Integrals in Conservative and Non-conservative Vector Fields, Part 2
zhlédnutí 568Před 4 lety
Line Integrals in Conservative and Non-conservative Vector Fields, Part 2
Line Integrals in Conservative and Non-conservative Vector Fields, Part 1
zhlédnutí 1,5KPřed 4 lety
Line Integrals in Conservative and Non-conservative Vector Fields, Part 1
MAT 125 Lesson 14: Fermat's Little Theorem, Modular Arithmetic
zhlédnutí 1,4KPřed 4 lety
MAT 125 Lesson 14: Fermat's Little Theorem, Modular Arithmetic
MAT 125 Lesson 13: Functions and Cardinality
zhlédnutí 2,5KPřed 4 lety
MAT 125 Lesson 13: Functions and Cardinality
Conditional Probability and Medical Diagnosis - UPDATED
zhlédnutí 1,1KPřed 4 lety
Conditional Probability and Medical Diagnosis - UPDATED
Writing Functions as Power Series, Part 2
zhlédnutí 208Před 4 lety
Writing Functions as Power Series, Part 2
Writing Functions as Power Series, Part 1
zhlédnutí 524Před 4 lety
Writing Functions as Power Series, Part 1
Conditional Probability and Medical Diagnosis
zhlédnutí 1,3KPřed 4 lety
Conditional Probability and Medical Diagnosis
soundtrack is distracting, despite I like the music. Fast forwarded to catch essentials and bye. Good review.
132 is basically (60 × 2) + (10 + 2) 120 +12 = 132
the video is over when he says earth orbiting the sun 🤣, you deserved a thumbs down for being coward and telling lies.
absolutely fantastic video. kudos.
Problem number 2 is really interesting. When the question is first shown on the screen at the start, it is A ∩ (B ∪ C) and (A ∩ B) ∪ (A ∩ C) around 24 second mark. However When we go to solve it, around the 9:30 mark it changed to A ∩ (B ∪ C) and A ∪ (B ∩ C) . I believe that A ∩ (B ∪ C) and (A ∩ B) ∪ (A ∩ C) is equal while A ∩ (B ∪ C) and A ∪ (B ∩ C) is not. I was coming up with a different answer and I believe that to be the reason why. That being said, this is still an excellent video and explains the concepts very well.
There's another error in Example 4: Cook could also be at 8.5 degrees North. lat = e - 90 + d and that would be valid too.
thanks for the feedback, but I think you are making an error by using lat = e - 90 + d. It should be either 90-e+d (northern hemisphere, and the choice for Cook) or 90-e-d (southern hemisphere) so this does require knowing which hemisphere you are in, but there are many natural cues for that.
@@csvaughen Your second formula doesn't reflect signs very well. I watched the derivation you provided and noticed that in your 'southern hemisphere' example you take positive theta for a latitude south of the Equator. So using your second formula 90-e-d, you get -8.5 deg, but since you considered theta positive for southern latitudes, then -8.5 deg would be 8.5 deg North. Also, one more thing: The criterion that decides which formula to use is NOT whether you are N or S of the Equator but rather whether you are N or S of 22.9 degrees (the parallel corresponding to the declination). It would be as you say when dec=0 (on the equinoxes).
But very good video for learning Thanks very much!
Longtitude example 3 looks to be a wrong calculation to get 75 degrees : 7 hours x15 degree/hour 105 degrees
yes, very true
Excellent and informative video. The multiple approaches e not 2.8 as the time subintervals go to infinity over the year.
nice game and lecture
Great job Scott and Alexis !! Definitely want to look at doing internship work at Lockheed Martin - they have hired many of our students and many more have interned at some point in their academic careers.
There is already a certain asymmetry between winning and losing, a shift in the direction of loss even if I win the same percentage as I lose. If I start with $100 and gain 1% (101% = $101), then lose 1% (101*99%=99.99), the end result is -1Cent loss.
yes, I've always found that result interesting, equal percent gains and losses cause a long term loss over time. Nevertheless, that does not change the results derived here.
Very good, I just wish I could follow along and understand it.
thanks, I can try answering any questions, this is a newer video on same topic czcams.com/video/-6irdqOoO-8/video.html
THANKS YOU FOR SHARING THIS VIDEO
THANKS YOU FOR SHARING THIS VIDEO
THANKS YOU FOR SHARING THIS VIDEO
THANKS YOU FOR SHARING THIS VIDEO
Thank you very very very veeeery very much!!!!!
Can You provide a videó about Nanson Method for The voting even it isn't used anymore
Hi, thank you for your comment- I'm sorry, I'm not even familiar with the Nanson method - had to look that one up - interesting - a hybrid method!
Thank you for this wonderful explanation and demonstration! It will make my appreciation of the clock so much great when I visit next month.
What If: the three bodies are of different nature / substance? Like: Human - AGI - ASI Physical - Digital - Quantum At the same they are of similar natu as they "contain" each other. Just following generally different rules of behaviour. This is a pure speculation though.
yes, fascinating to think about: the "bodies" measured by something other than mass and the "interactions" governed by something other than gravity. It seems like going from 2 to 3 bodies would always significantly complicate the interactions and this example, with mass and gravity, is just one illustration of that.
Ll l
It would be incredible to see this in relation to true earth (i.e. geocentric ) Thank The Lord Our ancestors were not cosmologically deceived 🙏🏻
❤
Thanks really helpful for my science fair
czcams.com/video/fzyNtBe1H5U/video.html
Excellent video, its a thing of past but must know. Now they use gps, speed of light, lasers and atomic clocks for high accuracy using advanced matrixes.
are you sure that declaration is 23.45 at tropic of cancer? what about 23.5?
Thank you for this!
شكرا جزيلا🔥❤️❤️😮💨
So thrilled to have stumbled upon your channel. It's a gold mine for an aerospace engineering student like me diving into Space Mechanics. Thank you for this amazing work!
😂😂 didn't expect the medical questions 🎉🎉 much needed this thanks.
Thank you for this creation. I am in the process of developing a semester elective Orbital Mechanics course for high school and plan to incorporate KSP into the class. Your workbook and videos are an inspiration and will help inform the lessons and activities I present to my classes. Cheers!
Awesome!! So happy to read this - exactly what I made this for - what lucky students to have you as a teacher and to have such an opportunity in high-school
appreciate
Love this series! i hope you continue making more of these!
Thank you, only here is a little mistake: At time 30:13, instead of 100-2 should be 100-4, as these are two tickets, both costing 2+2=4
thanks for your comment, however (100-2) is correct because, in that event, you win $100 and pay for one ticket which costs $2, thus the profit would be $98. The chance of winning the $100 prize is based on 2 tickets out of 500 so the probability is 2/500. Still, we calculate outcome of that event based on winning one ticket (100 - 2) because question asks for expected value of a single ticket.
It's the clock telling the truth.
I watched the whole thing, and actually understood it, very well explained! I think I understand more the novel plot now. I can also imagine this is one of the simple ways to simulate this, and relies on a bunch of assumptions. It would be cool to show this on some TV screen in the depths of a funky Amsterdam coffeeshop.
thank you!! and yes - true - probably would have to be a mathematician from a higher dimensional space
@1:02:51 Philadelphia should be 75.2W, not 74.2W
Bla bla …get onboard,draw your navigation on the inside of the sphere,you can see your destination on the other side of the sphere like the celestial sphere with the earth at the center and the starz on the inner surface of the sphere like a thin piece of tracing paper you can see through either side and then imagine cracking an egg looking inside a point on the horizon where the egg remains joined you can tracker ball on the surface of the southern hemisphere and the northern hemisphere of the eggshell represents the sky the viewing plane is the space opened by cracking the egg. The cosmic perspective
Applications of graph theory: 31:24
Thank youu so much!!!
What is the probability with 100 students that there are 15 pairs of birthdays and one trio? Secondly a question I can not begin to answer: what is the expected distribution among 365 students? Computer simulation? More than one right answer?
hmm, interesting questions... I once had a class that had 3 pairs of matching birthdays, and I was included in one of the pairs. I don't think I've seen a trio match before, that's fun...seems like you'd really need a big group for any chance of that... next time I teach the stat class, this could be a fun thing to explore, yes, with a computer simulation, that would be fun
Am an elderly retired physician. The answers to the 2 , 3,4 and 5 persons’ birthday problems ,at P= 0.50 are well known:23, 88, 187 and 314. How big was your class with three pairs?
I calculate that the largest group with a trio - without any pairs-is 34 with a P value of.01107876. Throw in 1 pair and the P value rises to .061696.
The problem above with 100 folks, 15 pairs and 1 trio gave me on my calculator P= .0160515. Took 3 1/2 minutes. How is it done in the real world?
@@alanrapoport2090 wow, this is great work, my class with 3 pairs was probably around 25 students.... honestly, I haven't really done any work on this topic beyond the basics I put into this video... and next, I'm not clear what you mean by "largest group with a trio without any pairs"... is the P value for this the probability of getting a trio (and no pairs) when you have 34 total people? Anyway, definitely this is a fantastic past time! I'm glad you found my video and found it interesting! I'll have to look up the 3,4 and 5 person b-day problems!
Thank yo Christopher. I have been wanting to find a way to determine both latitude and longitude by the sun. Great explanation and thanks for making the post on the two multiplication errors in examples 3 and 4. I am glad you did. Admitting the errors proves we are all human! Keep up the fantastic content.
This was extremely helpful; i was so stuck after listening to my college lecture. You broke it down better than my professor, so thank you
how do you set this problem up for the tank being an ellipse?
YOU'RE A MESSIAH
Thanks professor. Now I know enough logic to become a lawyer
This is very helpful! The usual method of explaining the eigenvalues of the state space representation in MatLab isn't intuitive for estimating the phugoid mode. Always good to do hand calculations rather than just trusting a more advanced model.