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Dynamics 2

Mathematical modeling & analysis of rigid bodies

Mark Misin Engineering Ltd

How do you get a mathematical model for a system like a rotating wind turbine or a spinning gyroscope that you can later use in other fields, such as control systems?

Would you like to know how to analyze satellite motion using angular momentum and how to take advantage of work and energy to deal with complicated objects in a very easy way?

Would you like to learn how to take a simple vibrating system and describe its motion using Newton laws and Lagrange?

Read more

How do you get a mathematical model for a system like a rotating wind turbine or a spinning gyroscope that you can later use in other fields, such as control systems?

Would you like to know how to analyze satellite motion using angular momentum and how to take advantage of work and energy to deal with complicated objects in a very easy way?

Would you like to learn how to take a simple vibrating system and describe its motion using Newton laws and Lagrange?

All that and much more, I will teach you here, in the course: Engineering Mechanics: Dynamics part 2 - Mathematical modeling and analysis of rigid bodies.

My name is Mark, and in this course, I will make sure that you will be fully equipped to model and analyze rigid bodies mathematically.

Knowing how to model rigid bodies is a "must" in engineering.

I have 3  control systems courses where I teach advanced controllers for autonomous cars and UAV-s. The basis for building a good controller is to have a good mathematical model.

In those courses, when I build those models, I rely heavily on topics taught here, such as inertia matrix (inertia tensor) and rotating frames.

For rigid bodies in 2D and 3D, we will cover kinematics, dynamics, work, energy, Lagrange, impulse and momentum.

You will get lots of problem solving, but you will also understand the intuition and reasoning behind the concepts.

Take a look at some of my free preview videos, and if you like what you see, ENROLL NOW, and let's get started.

See you inside.

Enroll now

What's inside

Syllabus

In this section, we will learn how to solve the problems involving the kinematics of rigid bodies.
Intro to the course!
Translation VS Rotation VS General plane motion
Read more
Translational motion
Intro to rotation about fixed axis
The pulleys with a belt problem - exercise
The pulleys with a belt problem - solution 1
The pulleys with a belt problem - solution 2
Rotating disk - exercise
Rotating disk - solution
The gear mechanism problem - exercise
The gear mechanism problem - solution
General plane motion - intro 1
General plane motion - intro 2
The two link piston motion - exercise
The two link piston motion - solution
The disk & link lock mechanism - exercise
The disk & link lock mechanism - solution
Separating general plane motion into translation & rotation - (velocities)
The gear rack, wheel, and the piston problem - exercise
The gear rack, wheel, and the piston problem - solution
IC - Instantaneous Center of zero velocity - intro
The truck and the rolling pipe problem - exercise
The truck and the rolling pipe problem - solution
The 3 link angular velocity problem - exercise
The 3 link angular velocity problem - solution (method 1)
The 3 link angular velocity problem - solution (method 2)
Separating general plane motion into translation & rotation - (accelerations)
The accelerations of the rotating wheel, link and piston - exercise
The accelerations of the rotating wheel, link and piston - solution 1
The accelerations of the rotating wheel, link and piston - solution 2
The accelerations of a translating wheel & the link - exercise
The accelerations of a translating wheel & the link - solution 1
The accelerations of a translating wheel & the link - solution 2
The accelerations of a translating wheel & the link - solution 3
The IC point on a pulley - exercise
The IC point on a pulley - solution
Follow up!
Here, you will learn about 3D kinematics and rotating frames
A 3D disk, rod, and collar problem - exercise
A 3D disk, rod, and collar problem - solution
Rotating frames - intro 1
Rotating frames - intro 2
Rotating frames - inertial VS body frame unit vectors
A 2D rotation matrix derivation
Deriving velocity & acceleration vectors using rotating frames
Moving collar on a rotating rod problem - exercise
Moving collar on a rotating rod problem - solution 1
Moving collar on a rotating rod problem - solution 2
A 3D satellite dish problem - exercise
A 3D satellite dish problem - solution 1
A 3D satellite dish problem - solution 2
A 3D satellite dish problem - solution 3
Proof that angular displacements are not vectors
A rotating motor problem - exercise
A rotating motor problem - solution 1
A rotating motor problem - solution 2
A rotating motor problem - solution 3
In this section, you will learn how to apply the Newton laws to rigid bodies and how the objects behave as a result of that.
Mass moments of inertia - intro
Parallel - Axis theorem - derivation
Radius of gyration & composite bodies - mass moments of inertia calculation
Mass moment of inertia of a cone - exercise
Mass moment of inertia of a cone - solution 1
Mass moment of inertia of a cone - solution 2
Composite body: sphere & rod - exercise
Composite body: sphere & rod - solution
Thin wheel & 4 spokes - exercise
Thin wheel & 4 spokes - solution
A plate with a hole - exercise
A plate with a hole - solution
Intro to translational motion - rectilinear & curvlinear translation
An airplane forward acceleration problem - exercise
An airplane forward acceleration problem - solution 1
An airplane forward acceleration problem - solution 2
The bicycle braking problem - exercise
The bicycle braking problem - solution
The pipe and truck bed problem - exercise
The pipe and truck bed problem - solution
The crane & the hydraulic cylinder problem - exercise
The crane & the hydraulic cylinder problem - solution
The curvelinear translation of a block problem - exercise
The curvelinear translation of a block problem - solution
Rotation about fixed axis & the equations of motion - intro
The pendulum problem - exercise
The pendulum problem - solution 1
The pendulum problem - solution 2
The two gear problem - exercise
The two gear problem - solution
The kinetic friction & a pulley problem - exercise
The kinetic friction & a pulley problem - solution
Two block and a pulley problem - exercise
Two block and a pulley problem - solution
General plane motion - intro
The spool on the inclined surface problem - exercise
The spool on the inclined surface problem - solution
Static VS kinetic friction for a wheel - exercise
Static VS kinetic friction for a wheel - solution
A concrete culvert on a truck problem - exercise
A concrete culvert on a truck problem - solution

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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 Dynamics 2: Mathematical modeling & analysis of rigid bodies with these activities:
Review Statics
Reinforce your understanding of statics principles, which are foundational for understanding the dynamics of rigid bodies.
Browse courses on Statics
Show steps
  • Review key concepts like equilibrium and free body diagrams.
  • Work through example problems from your statics textbook.
  • Focus on problems involving forces and moments.
Read 'Engineering Mechanics: Dynamics' by Hibbeler
Supplement the course material with a widely used textbook on dynamics to gain a deeper understanding of the concepts.
View Engineering Mechanics: Dynamics, SI Units on Amazon
Show steps
  • Obtain a copy of 'Engineering Mechanics: Dynamics' by Hibbeler.
  • Read the chapters relevant to the course syllabus.
  • Work through the example problems in the book.
Solve Kinematics Problems
Improve your problem-solving skills by working through a variety of kinematics problems involving rigid bodies.
Show steps
  • Find a collection of kinematics problems online or in a textbook.
  • Solve problems related to translation, rotation, and general plane motion.
  • Check your solutions against the provided answers.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Read 'Classical Mechanics' by John R. Taylor
Gain a deeper understanding of Lagrangian mechanics by studying a textbook that focuses on theoretical foundations.
View Student Solutions to Accompany Taylor's an... on Amazon
Show steps
  • Obtain a copy of 'Classical Mechanics' by John R. Taylor.
  • Read the chapters on Lagrangian and Hamiltonian mechanics.
  • Work through the example problems in the book.
Create a Video Explaining Inertia Tensor
Solidify your understanding of the inertia tensor by creating a video explaining its concept and calculation.
Show steps
  • Research the concept of the inertia tensor.
  • Write a script explaining the concept in simple terms.
  • Record a video explaining the concept, including examples.
  • Edit the video and upload it to a video-sharing platform.
Create a Presentation on Rotating Frames
Deepen your understanding of rotating frames by creating a presentation explaining the concept and its applications.
Show steps
  • Research the concept of rotating frames and their applications.
  • Create a presentation outlining the key concepts and examples.
  • Practice delivering the presentation to a friend or colleague.
Model a Double Pendulum
Apply your knowledge of dynamics to model the motion of a double pendulum using Lagrangian mechanics.
Show steps
  • Derive the equations of motion for a double pendulum using Lagrange's equations.
  • Implement the equations of motion in a programming language like Python.
  • Simulate the motion of the double pendulum and visualize the results.

Career center

Learners who complete Dynamics 2: Mathematical modeling & analysis of rigid bodies will develop knowledge and skills that may be useful to these careers:
Robotics Engineer
A Robotics Engineer designs, builds, and tests robots for various applications. This course, with its focus on mathematical modeling and analysis of rigid bodies, directly applies to the understanding of robotic systems. A Robotics Engineer needs to create accurate models of robot movement. Studying translation versus rotation, general plane motion, and 3D kinematics, as covered in this course, is highly applicable. For example, this course may improve a Robotics Engineer's ability to model the movement of robotic arms or the stability of mobile robots, enhancing their design and control capabilities.
See salaries and explore the career path for Robotics Engineer
Aerospace Engineer
An Aerospace Engineer designs aircraft, spacecraft, and related systems. The ability to mathematically model and analyze rigid bodies is crucial in aerospace engineering. An Aerospace Engineer can leverage the principles taught in this course to analyze satellite motion using angular momentum and understand how work and energy affect spacecraft dynamics. The course's coverage of 3D kinematics and rotating frames is directly relevant to modeling the behavior of satellites and other spacecraft as well. This course may improve an Aerospace Engineer's ability to design stable and efficient aerospace systems.
See salaries and explore the career path for Aerospace Engineer
Mechanical Engineer
A Mechanical Engineer designs and oversees the manufacturing of many different devices. This course is very helpful for a Mechanical Engineer. It provides the mathematical modeling and analysis skills necessary for dealing with rigid body dynamics. A Mechanical Engineer can apply the principles of work, energy, impulse, and momentum. This course's emphasis on problem-solving and understanding the intuition behind the concepts should be quite helpful. This also gives a Mechanical Engineer a solid grasp of topics like inertia matrices and rotating frames.
See salaries and explore the career path for Mechanical Engineer
Control Systems Engineer
A Control Systems Engineer designs and implements systems that control the behavior of other devices. The most important requirement for a Control Systems Engineer is to have a good mathematical model, or to analyze the mathematical models provided by others. This course teaches the modeling of rigid bodies mathematically. It is a "must" in engineering. Control Systems Engineers can then leverage these mathematical models to do their own work. Topics in this course, such as inertia matrix and rotating frames are highly relevant.
See salaries and explore the career path for Control Systems Engineer
Automotive Engineer
An Automotive Engineer designs and develops vehicles and their components. Automotive engineering relies heavily on understanding rigid body dynamics, making this course quite valuable. An Automotive Engineer can use the concepts emphasized in this course to model vehicle suspension systems, analyze the motion of engine components, and optimize vehicle stability. The course's focus on kinematics, dynamics, work, energy will be beneficial. Moreover, the problem-solving approach taught may improve the Automotive Engineer's ability to address real-world challenges in vehicle design.
See salaries and explore the career path for Automotive Engineer
Simulation Engineer
A Simulation Engineer creates computer models of physical systems to predict their behavior. This course will provide the mathematical foundation needed to accurately simulate rigid body dynamics. A Simulation Engineer can leverage the knowledge gained to develop simulations of everything from vehicle suspensions to robotic arms. The concepts of kinematics, dynamics, and energy, covered in the course, are essential for creating realistic and reliable simulations. The problem solving skills taught in this course will also be quite useful as well.
See salaries and explore the career path for Simulation Engineer
Wind Energy Engineer
A Wind Energy Engineer designs and maintains wind turbines and wind farms. This course, with its emphasis on mathematical modeling and analysis of rigid bodies, is directly relevant. A Wind Energy Engineer can apply the concepts learned to model the behavior of rotating wind turbine blades, analyze the forces acting on the turbine structure, and optimize the design for maximum energy capture. The course's focus on kinematics, dynamics, work, and energy are quite helpful. The rotating frames and general plane motion principles can also be applied.
See salaries and explore the career path for Wind Energy Engineer
Structural Engineer
A Structural Engineer designs and analyzes structures to ensure their stability and safety. This course may be useful for a Structural Engineer. Structural Engineering involves understanding how rigid bodies behave under different loads and conditions. The course's coverage of dynamics, work, and energy could be beneficial. By understanding these principles, a Structural Engineer may enhance their ability to design robust and reliable structures. A Structural Engineer may also improve finite element analysis skills.
See salaries and explore the career path for Structural Engineer
Research Scientist
A Research Scientist conducts research to advance knowledge in a specific field. For a Research Scientist focusing on areas like robotics, aerospace, or mechanical engineering, this course may be useful. The course's emphasis on mathematical modeling and analysis of rigid bodies provides a strong foundation for conducting advanced research. The Research Scientist can then apply the problem-solving skills taught to real-world problems. This course may enhance a Research Scientist's ability to develop new theories and technologies.
See salaries and explore the career path for Research Scientist
Test Engineer
A Test Engineer designs and executes tests to ensure the quality and performance of products. This course may be helpful for a Test Engineer because understanding the underlying dynamics of rigid bodies helps in designing effective tests. The Test Engineer can use the principles taught in the course to analyze the data collected during testing and identify potential issues. The course's coverage of kinematics, dynamics, work, and energy may be beneficial. This may also help the Test Engineer understand the limitations of design.
See salaries and explore the career path for Test Engineer
Product Designer
A Product Designer designs new products and improves existing ones. Understanding the dynamics of rigid bodies can inform design decisions, especially for products involving motion or mechanical components. The course's coverage of topics like kinematics and dynamics may be useful. This also helps the designer grasp the implications of the product in motion. By understanding these principles, a Product Designer may enhance their ability to create innovative and functional products.
See salaries and explore the career path for Product Designer
Instrumentation Engineer
An Instrumentation Engineer designs, develops, and maintains instruments and control systems. This course may be useful for an Instrumentation Engineer. Understanding the mathematical models of rigid bodies helps in designing accurate and reliable sensors. By analyzing the dynamics of the systems being measured, Instrumentation Engineers can improve the performance. The course's coverage of relevant topics such as rotating frames and mass moment of inertia can be helpful in complex designs.
See salaries and explore the career path for Instrumentation Engineer
Manufacturing Engineer
A Manufacturing Engineer improves manufacturing processes to enhance efficiency and quality. This course may be helpful for a Manufacturing Engineer. Understanding the motion of rigid bodies helps in optimizing the design of manufacturing equipment and processes. The course's knowledge on dynamics can be applied to the design of robotic assembly lines. This also helps the designer understand the overall dynamics of the system.
See salaries and explore the career path for Manufacturing Engineer
Data Scientist
A Data Scientist analyzes large datasets to extract insights and inform decisions. This course may be useful for a Data Scientist who focuses on areas such as robotics or physics simulations. The course's emphasis on mathematical modeling can be useful in the cleaning and analysis of data. Principles such as energy and momentum can also be applied to the data. This course may enhance a Data Scientist's understanding of data.
See salaries and explore the career path for Data Scientist
Technical Consultant
A Technical Consultant provides expert advice and guidance to clients on technical matters. This course can be useful for a Technical Consultant who advises clients in industries such as aerospace, automotive, or manufacturing. The course's coverage of relevant topics such as rotation and kinematics may be beneficial. Consultants can apply knowledge from the course to better understand client problems and propose effective solutions. This course may also enhance a Technical Consultant's ability to communicate complex technical concepts.
See salaries and explore the career path for Technical Consultant

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Dynamics 2: Mathematical modeling & analysis of rigid bodies.
Engineering Mechanics: Dynamics, SI Units
Save
Comprehensive resource for dynamics, covering kinematics and kinetics of particles and rigid bodies. It provides numerous examples and practice problems, making it an excellent reference for this course. It is commonly used as a textbook in university-level dynamics courses. Reading this book will provide additional depth and breadth to the course material.
Engineering Mechanics: Dynamics, SI Units
Paperback
Check
Engineering Mechanics: Dynamics, SI Units
Kindle Edition
Check
Student Solutions Manual to Accompany Taylor's...
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Provides a clear and accessible introduction to Lagrangian and Hamiltonian mechanics. It is particularly helpful for understanding the theoretical foundations of dynamics. While not strictly necessary for the course, it provides a deeper understanding of the underlying principles and is often used as a textbook in advanced undergraduate and graduate courses.
Student Solutions to Accompany Taylor's an...
Paperback
$$

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Effort
15 total hours
Via
Udemy
Instructor
Mark Misin Engineering Ltd
Language
English
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