Optimal control

Zermelo's navigation problem

In mathematical optimization, Zermelo's navigation problem, proposed in 1931 by Ernst Zermelo, is a classic optimal control problem that deals with a boat navigating on a body of water, originating from a point to a destination point . The boat is capable of a certain maximum speed, and the goal is to derive the best possible control to reach in the least possible time. Without considering external forces such as current and wind, the optimal control is for the boat to always head towards . Its path then is a line segment from to , which is trivially optimal. With consideration of current and wind, if the combined force applied to the boat is non-zero the control for no current and wind does not yield the optimal path. (Wikipedia).

Zermelo's navigation problem
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Equilateral Triangles Problem

GeoGebra Link: https://www.geogebra.org/m/f5zgupmz

From playlist Geometry: Challenge Problems

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How to find the bearing and distance a boat travels using trigonometry

👉 Learn how to solve the word problems with trigonometry. Word problems involving angles, including but not limited to: bearings, angle of elevations and depressions, triangles problems etc are solved using trigonometry. To be able to solve these problems it is important that you have a gr

From playlist Evaluate Inverse Trigonometric Functions

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Regular Polygon Phenomena!

GeoGebra Link: https://www.geogebra.org/m/ketkkfuj

From playlist Geometry: Challenge Problems

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Concave Quadrilateral Craziness! (GoGeometry Action 80)

Link: https://www.geogebra.org/m/T4axJRwY

From playlist Geometry: Challenge Problems

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Gravitation (13 of 17) Orbital Velocity at the Surface of the Earth

This videos explains how to determine the velocity that an object, one meter above the Earth's surface, must be projected horizontally so that it will go all of the way around the Earth and come back to the same place. Calculate orbital velocity one meter above the Earth's surface. The o

From playlist Gravitation: Orbital Velocity, Orbital Period, Potential Energy, Kinetic Energy, Mass and Weight

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Trigonometry: Harmonic Motion Word Problem

In this video we do a harmonic motion word problem. A weight is attached to a spring and we have to find the max height above equilibrium(which is the amplitude in this case), period, frequency, and the time it takes to reach the maximum height. If you enjoyed this video please consider l

From playlist Trigonometry Problems

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How to find the distance a car travels with changing angle

👉 Learn how to solve the word problems with trigonometry. Word problems involving angles, including but not limited to: bearings, angle of elevations and depressions, triangles problems etc are solved using trigonometry. To be able to solve these problems it is important that you have a gr

From playlist Evaluate Inverse Trigonometric Functions

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Special Topics - GPS (53 of 100) Ionosphere Delay

Visit http://ilectureonline.com for more math and science lectures! http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will take a closer look at the effects of ionosphere. There is a delay of the signal as it travels through the ionosphere. The signal is part

From playlist SPECIAL TOPICS 2 - GPS

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How ISPs Violate the Laws of Mathematics

Get a free trial of Audible at https://audible.com/minutephysics or by texting 'minutephysics' to 500500 Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysic

From playlist MinutePhysics

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Zermelo Fraenkel Choice

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We dicuss the axiom of chice, and sketch why it is independent of the other axioms of set theory. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50f

From playlist Zermelo Fraenkel axioms

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Zermelo Fraenkel Separation and replacement

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of separation and replacement and some of their variations. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG2oi

From playlist Zermelo Fraenkel axioms

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Zermelo Fraenkel Foundation

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of foundation, which says that the membership relation is well founded, and give some examples of the bizarre things that can happen if sets are allowed to be non-well-founded. For

From playlist Zermelo Fraenkel axioms

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Topology Without Tears - Video 2b - Infinite Set Theory

This is part (b) of Video 2, the second in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost from www.topologywithouttears.net

From playlist Topology Without Tears

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Zermelo Fraenkel Infinity

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of infinity, and give some examples of models where it does not hold. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG

From playlist Zermelo Fraenkel axioms

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Zermelo Fraenkel Pairing and union

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axioms of pairing and union, the two easiest axioms of ZFC, and consider whether they are really needed. For the other lectures in the course see https://www.youtube.com/playlist?list=PL

From playlist Zermelo Fraenkel axioms

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Zermelo Fraenkel Powerset

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the powerset axiom, the strongest of the ZF axioms, and explain why the notion of a powerset is so hard to pin down precisely. For the other lectures in the course see https://www.youtube.com

From playlist Zermelo Fraenkel axioms

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The Music Of Flight

Poetic motion of a bird in flight set to original music

From playlist My music video's

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Equation Informed and Data-Driven Tools for Data-Assimilation and Optimal....by Luca Biferale

Program Turbulence: Problems at the Interface of Mathematics and Physics (ONLINE) ORGANIZERS: Uriel Frisch (Observatoire de la CĂ´te d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (Indian Institute of Science, Bengaluru) DATE: 07 December 202

From playlist Turbulence: Problems at The Interface of Mathematics and Physics (Online)

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AWESOME Brachistochrone problem II

In this video, i set up and solve the brachistochrone problem, which involves determining the path of shortest travel in the presence of a downward gravitational field. This is done using the techniques of calculus of variations, and it will turn out that the brachistochrone can be represe

From playlist MECHANICS

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Topology Without Tears - Video 2c - Infinite Set Theory

This is the final part, part (c), of Video 2 in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost at www.topologywithouttears.net

From playlist Topology Without Tears

Related pages

Mathematical optimization | Calculus of variations | Euler–Lagrange equation | Optimal control