Flight Dynamics with Tensors from Udemy

Flight dynamics is undergoing a shift from vectors to tensors, taking advantage of the ever increasing computer power to design and analyze complex aerospace systems. The physics are modeled by tensors independent of coordinate systems. Then the tensors are converted to matrices by introducing coordinate systems and evaluated by one of the many matrix computer tools.

This course introduces the novice to tensor flight dynamics, requiring only basic skills in matrix algebra and differential equations. The fundamentals of tensor algebra are introduced by modeling geometrical relationships of expended boosters landing on barges with their related coordinate transformations. As time enters the study, the new rotational time derivative enables kinematics to be formulated independent of coordinate systems in a truly tensorial format, applied to pilots in centrifuges and attitude determination of aircraft. Point-mass trajectories, also called three-degrees-of freedom trajectories, are derived for rockets, hypersonic vehicles, UAVs; and full-up, six-degrees-of-freedom equations lead to the evaluation of the transient responses of missiles and aircraft in state-space format.

The course is supported by the text book “Introduction to Tensor Flight Dynamics”, published in 2020 by the instructor at Amazon. It provides more details on how to derive the equations of motion from Newton’s and Euler’s laws and features many problems derived from aerospace applications, some of them to be solved with MATLAB® or other matrix processors.

What's inside

Learning objectives

Master the new approach to flight dynamics
Expose yourself to cartesian tensors
Learn how to convert tensors into matrices

Express the equations of motion in matrices
Program the matrix equations in matlab or python

Master the new approach to flight dynamics
Expose yourself to cartesian tensors
Learn how to convert tensors into matrices
Express the equations of motion in matrices
Program the matrix equations in matlab or python

Syllabus

Introduction

You will be surprised what tensors contribute to flight dynamics

Modeling geometrical relationships of expended boosters landing on barges

Get acquainted with tensors by a simple example

Now you dive into tensor algebra more deeply

Coordinate systems turn tensors into matrices for computation

Relative and differential velocities of missiles engaging targets

A new time derivative that keeps tensors to remain tensors

Here you derive the famous Coriolis transformation

From angular rates to the attitudes of rockets and aircraft

Trajectories of satellites, rockets, UAV, and hypersonic vehicles

Newton is all you need to know to compute trajectories

Astronauts, booster rockets, and hypersonic vehicles fly in inertial space

Now we come down to Earth

Missiles, rockets, and aircraft dynamics in six degrees-of-freedom state-space equations

Jump into six degrees-of-freedom with Newton and Euler

Analyze their dynamics with state-space equations

You will study the dutch-roll dynamics of the venerable B747

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches students to apply tensors to understand flight dynamics

Designed for students with backgrounds in matrix algebra and differential equations

Provides comprehensive coverage of tensor flight dynamics, from basic concepts to advanced applications

Emphasizes the conversion of tensors into matrices for practical implementation

Taught by Dr. Peter H. Zipfel, an expert in flight dynamics with extensive experience in the field

Recommended for students pursuing careers in aerospace engineering or related fields

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Flight Dynamics with Tensors with these activities:

Review basic matrix algebra and differential equations

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Refresh your knowledge of matrix algebra and differential equations, which are essential prerequisites for this course.

Browse courses on Matrix Algebra

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Take practice problems to test your understanding.
Go over your notes from previous courses or textbooks.

Organize your course materials

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Ensure a smoother learning experience by keeping your notes, assignments, and other course materials organized.

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Create a dedicated folder or notebook for the course.
File and organize your materials systematically.

Read 'Introduction to Tensor Flight Dynamics'

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Expand your knowledge of tensor flight dynamics before the course by reading the recommended textbook, which provides in-depth derivations and additional problems.

View C++ Aerospace Workshop in Two Days, 2nd Edition... on Amazon

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Purchase or borrow the textbook.
Read the assigned chapters and take notes.
Solve the practice problems to reinforce your understanding.

Five other activities

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Explore MATLAB or Python for tensor computations

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Become familiar with MATLAB or Python to prepare for converting tensors into matrices, a key skill in this course.

Browse courses on MATLAB

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Find tutorials or online courses on MATLAB or Python.
Follow the tutorials and practice writing basic code.

Watch tutorials on tensor algebra

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Review the basics of tensor algebra through guided tutorials to strengthen your foundation before the course begins.

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Identify online tutorials on tensor algebra.
Watch the tutorials and take notes on the key concepts.

Solve tensor algebra practice problems

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Sharpen your tensor algebra skills by working through practice problems.

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Find practice problems online or in textbooks.
Solve the problems and check your answers.
Review the solutions to identify areas for improvement.

Join a study group for tensor flight dynamics

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Connect with peers and engage in discussions to deepen your understanding of the course material.

Browse courses on Flight Dynamics

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Find or create a study group.
Discuss lecture topics, homework assignments, and projects.

Model a simple flight scenario using tensors

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Apply your understanding of tensors to a practical flight scenario, which will help you solidify your knowledge.

Browse courses on Flight Dynamics

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Define the problem and identify the relevant parameters.
Create a tensor model to represent the flight scenario.
Simulate the flight scenario using your model.
Analyze the results and draw conclusions.

Career center

Learners who complete Flight Dynamics with Tensors will develop knowledge and skills that may be useful to these careers:

Aerospace Engineer

Aerospace Engineers apply the principles of aerodynamics, thermodynamics, and mechanics to the design, development, testing, and operation of aircraft, spacecraft, and missiles. This course may be especially useful to those interested in the dynamics of aircraft and spacecraft, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Aerospace Engineer

Flight Test Engineer

Flight Test Engineers conduct tests to evaluate the performance and handling characteristics of aircraft. This course may be especially useful to those interested in understanding the dynamics of aircraft in flight, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Flight Test Engineer

Avionics Engineer

Avionics Engineers design, develop, and maintain the electronic systems used in aircraft, spacecraft, and missiles. This course may be especially useful to those interested in understanding the dynamics of aircraft and spacecraft, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Avionics Engineer

Control Systems Engineer

Control Systems Engineers design and develop systems to control the movement and operation of machines and vehicles. This course may be especially useful to those interested in understanding the dynamics of aircraft and spacecraft, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Control Systems Engineer

Robotics Engineer

Robotics Engineers design, develop, and maintain robots. This course may be especially useful to those interested in understanding the dynamics of robots, as it provides a foundation in tensor algebra and its application to flight dynamics.

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Systems Engineer

Systems Engineers design, develop, and maintain complex systems. This course may be especially useful to those interested in understanding the dynamics of complex systems, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Systems Engineer

Simulation Engineer

Simulation Engineers develop and use computer simulations to model and analyze the performance of systems. This course may be especially useful to those interested in understanding the dynamics of complex systems, as it provides a foundation in tensor algebra and its application to flight dynamics.

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Data Scientist

Data Scientists analyze data to extract insights and solve problems. This course may be especially useful to those interested in understanding the dynamics of complex systems, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve problems in business and industry. This course may be especially useful to those interested in understanding the dynamics of complex systems, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

Financial Analysts analyze financial data to make investment recommendations. This course may be especially useful to those interested in understanding the dynamics of financial markets, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Financial Analyst

Investment Analyst

Investment Analysts analyze investment opportunities to make recommendations to clients. This course may be especially useful to those interested in understanding the dynamics of financial markets, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Investment Analyst

Risk Manager

Risk Managers identify and assess risks to an organization. This course may be especially useful to those interested in understanding the dynamics of risk, as it provides a foundation in tensor algebra and its application to flight dynamics.

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Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. This course may be especially useful to those interested in understanding the dynamics of risk, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Actuary

Statistician

Statisticians collect, analyze, and interpret data to solve problems. This course may be especially useful to those interested in understanding the dynamics of data, as it provides a foundation in tensor algebra and its application to flight dynamics.

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Data Analyst

Data Analysts collect, analyze, and interpret data to solve problems. This course may be especially useful to those interested in understanding the dynamics of data, as it provides a foundation in tensor algebra and its application to flight dynamics.

See salaries and explore the career path for Data Analyst