Newton-Euler Equations for Rigid Body | Center of Mass & Inertia Tensor Worked Example | Lecture 10

Описание: Lecture 10 of a course on analytical dynamics (Newton-Euler, Lagrangian dynamics, and 3D rigid body dynamics). Rigid bodies made of a continuous mass distribution are considered. We write the formulas for the total mass and center of mass.

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0:00 Rigid bodies made of a continuous mass distribution are considered. We write the formulas for the total mass and center of mass.

We consider the example of a
7:59 flat triangular plate of uniform density and use integrals do determine the center of mass. We discuss the idea of decomposing our a complicated rigid body into simpler rigid bodies for purposes of calculating the mass moments (such as the location of the center of mass and the moment of inertia tensor).

22:40 Composite shapes: complicated rigid body approximated by simpler ones to estimate center of mass and moment of inertia

32:23 The Newton-Euler approach to rigid body dynamics is introduced, including Euler's 1st Law for translational motion (a.k.a., the "superparticle theorem") and Euler's 2nd Law for rotational motion (a.k.a., the rotational dynamics equation, Euler's rotational equation).

44:30 Parallels between the kinematic and dynamic equations of the translational and rotational motion of a rigid body.

52:37 The mass moments of a rigid body are summarized:
zeroth moment: total mass (3^0 = 1 number, scalar)
first moment: center of mass (3^1 = 3 numbers, vector)
2nd moment: moment of inertia (3^2 = 9 numbers, tensor)

We end with the writing of
59:41 Euler's 2nd Law, the rotational dynamics equation, in the body-fixed frame, and as a set of 3 first-order ODEs for the components of angular velocity.

► The entire playlist of videos for this course:
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► Class lecture notes (PDF) https://is.gd/ESM5314notes
and in OneNote form

► Textbook used:
Engineering Dynamics: A Comprehensive Introduction
by N. Jeremy Kasdin and Derek A. Paley
https://press.princeton.edu/books/har...

Lecture 2020-09-24, Fall 2020

Author's website:
http://shaneross.com

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📚Nonlinear Dynamics and Chaos
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📚Lagrangian and 3D Rigid Body Dynamics
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📚Hamiltonian Dynamics
https://is.gd/AdvancedDynamics

📚Center Manifolds, Normal Forms, and Bifurcations
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📚Space Vehicle Dynamics
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📚3-Body Problem Orbital Dynamics Course
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📚Space Manifolds
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