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

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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