Dynamics 2: Mathematical Modeling & Analysis Of Rigid Bodies

Use Math to analyze & model rigid body systems! Master kinematics, dynamics, work, energy, impulse, momentum & Lagrange!

What you'll learn

How to analyze the motion of rigid bodies using kinematics (2D & 3D)

How to analyze the motion of rigid bodies using dynamics (2D & 3D)

How to model rigid body systems mathematically

How to use work & energy principles to simplify working with complicated systems

How to use impulse & momentum principles to simplify working with complicated systems

How to apply the Lagrangian mechanics to systems subject to conservative forces

Requirements

Functions, Derivatives and Integrals from Calculus

The concepts from Statics such as: vectors, forces, moments, equilibrium and friction.

The concepts from particle Dynamics such as: kinematics, forces & moments, work, energy, impulse and momentum

Description

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!

Overview

Section 1: Kinematics of rigid bodies in 2D

Lecture 1 Intro to the course!

Lecture 2 Translation VS Rotation VS General plane motion

Lecture 3 Translational motion

Lecture 4 Intro to rotation about fixed axis

Lecture 5 The pulleys with a belt problem - exercise

Lecture 6 The pulleys with a belt problem - solution 1

Lecture 7 The pulleys with a belt problem - solution 2

Lecture 8 Rotating disk - exercise

Lecture 9 Rotating disk - solution

Lecture 10 The gear mechanism problem - exercise

Lecture 11 The gear mechanism problem - solution

Lecture 12 General plane motion - intro 1

Lecture 13 General plane motion - intro 2

Lecture 14 The two link piston motion - exercise

Lecture 15 The two link piston motion - solution

Lecture 16 The disk & link lock mechanism - exercise

Lecture 17 The disk & link lock mechanism - solution

Lecture 18 Separating general plane motion into translation & rotation - (velocities)

Lecture 19 The gear rack, wheel, and the piston problem - exercise

Lecture 20 The gear rack, wheel, and the piston problem - solution

Lecture 21 IC - Instantaneous Center of zero velocity - intro

Lecture 22 The truck and the rolling pipe problem - exercise

Lecture 23 The truck and the rolling pipe problem - solution

Lecture 24 The 3 link angular velocity problem - exercise

Lecture 25 The 3 link angular velocity problem - solution (method 1)

Lecture 26 The 3 link angular velocity problem - solution (method 2)

Lecture 27 Separating general plane motion into translation & rotation - (accelerations)

Lecture 28 The accelerations of the rotating wheel, link and piston - exercise

Lecture 29 The accelerations of the rotating wheel, link and piston - solution 1

Lecture 30 The accelerations of the rotating wheel, link and piston - solution 2

Lecture 31 The accelerations of a translating wheel & the link - exercise

Lecture 32 The accelerations of a translating wheel & the link - solution 1

Lecture 33 The accelerations of a translating wheel & the link - solution 2

Lecture 34 The accelerations of a translating wheel & the link - solution 3

Lecture 35 The IC point on a pulley - exercise

Lecture 36 The IC point on a pulley - solution

Lecture 37 Follow up!

Section 2: Kinematics in 3D + rotating frames for rigid bodies

Lecture 38 A 3D disk, rod, and collar problem - exercise

Lecture 39 A 3D disk, rod, and collar problem - solution

Lecture 40 Rotating frames - intro 1

Lecture 41 Rotating frames - intro 2

Lecture 42 Rotating frames - inertial VS body frame unit vectors

Lecture 43 A 2D rotation matrix derivation

Lecture 44 Deriving velocity & acceleration vectors using rotating frames

Lecture 45 Moving collar on a rotating rod problem - exercise

Lecture 46 Moving collar on a rotating rod problem - solution 1

Lecture 47 Moving collar on a rotating rod problem - solution 2

Lecture 48 A 3D satellite dish problem - exercise

Lecture 49 A 3D satellite dish problem - solution 1

Lecture 50 A 3D satellite dish problem - solution 2

Lecture 51 A 3D satellite dish problem - solution 3

Lecture 52 Proof that angular displacements are not vectors

Lecture 53 A rotating motor problem - exercise

Lecture 54 A rotating motor problem - solution 1

Lecture 55 A rotating motor problem - solution 2

Lecture 56 A rotating motor problem - solution 3

Section 3: Dynamics of rigid bodies in 2D

Lecture 57 Mass moments of inertia - intro

Lecture 58 Parallel - Axis theorem - derivation

Lecture 59 Radius of gyration & composite bodies - mass moments of inertia calculation

Lecture 60 Mass moment of inertia of a cone - exercise

Lecture 61 Mass moment of inertia of a cone - solution 1

Lecture 62 Mass moment of inertia of a cone - solution 2

Lecture 63 Composite body: sphere & rod - exercise

Lecture 64 Composite body: sphere & rod - solution

Lecture 65 Thin wheel & 4 spokes - exercise

Lecture 66 Thin wheel & 4 spokes - solution

Lecture 67 A plate with a hole - exercise

Lecture 68 A plate with a hole - solution

Lecture 69 Intro to translational motion - rectilinear & curvlinear translation

Lecture 70 An airplane forward acceleration problem - exercise

Lecture 71 An airplane forward acceleration problem - solution 1

Lecture 72 An airplane forward acceleration problem - solution 2

Lecture 73 The bicycle braking problem - exercise

Lecture 74 The bicycle braking problem - solution

Lecture 75 The pipe and truck bed problem - exercise

Lecture 76 The pipe and truck bed problem - solution

Lecture 77 The crane & the hydraulic cylinder problem - exercise

Lecture 78 The crane & the hydraulic cylinder problem - solution

Lecture 79 The curvelinear translation of a block problem - exercise

Lecture 80 The curvelinear translation of a block problem - solution

Lecture 81 Rotation about fixed axis & the equations of motion - intro

Lecture 82 The pendulum problem - exercise

Lecture 83 The pendulum problem - solution 1

Lecture 84 The pendulum problem - solution 2

Lecture 85 The two gear problem - exercise

Lecture 86 The two gear problem - solution

Lecture 87 The kinetic friction & a pulley problem - exercise

Lecture 88 The kinetic friction & a pulley problem - solution

Lecture 89 Two block and a pulley problem - exercise

Lecture 90 Two block and a pulley problem - solution

Lecture 91 General plane motion - intro

Lecture 92 The spool on the inclined surface problem - exercise

Lecture 93 The spool on the inclined surface problem - solution

Lecture 94 Static VS kinetic friction for a wheel - exercise

Lecture 95 Static VS kinetic friction for a wheel - solution

Lecture 96 A concrete culvert on a truck problem - exercise

Lecture 97 A concrete culvert on a truck problem - solution

Lecture 98 A rotating ladder on a truck - exercise

Lecture 99 A rotating ladder on a truck - solution

Lecture 100 A disk and a pulley problem - exercise

Lecture 101 A disk and a pulley problem - solution 1

Lecture 102 A disk and a pulley problem - solution 2

Lecture 103 A truck riding on another car problem - exercise

Lecture 104 A truck riding on another car problem - solution 1

Lecture 105 A truck riding on another car problem - solution 2

Section 4: Dynamics in 3D + inertia tensor + rotating frames for rigid bodies

Lecture 106 Intro to mass moments of inertia in 3D

Lecture 107 Intro to products of inertia in 3D

Lecture 108 Intro to inertia tensor & the generic moment equations

Lecture 109 Inertia tensor calculation for a cube problem - exercise

Lecture 110 Inertia tensor calculation for a cube problem - solution 1

Lecture 111 Inertia tensor calculation for a cube problem - solution 2

Lecture 112 Inertia tensor calculation for a cube problem - solution 3

Lecture 113 A rotating wind turbine moment calculation problem - exercise

Lecture 114 A rotating wind turbine moment calculation problem - solution 1

Lecture 115 A rotating wind turbine moment calculation problem - solution 2

Lecture 116 The gyroscope - intuition 1

Lecture 117 The gyroscope - intuition 2

Lecture 118 The gyroscope - mathematics - exercise

Lecture 119 The gyroscope - mathematics - solution 1

Lecture 120 The gyroscope - mathematics - solution 2

Lecture 121 The gyroscope - mathematics - solution 3

Section 5: Work & energy for rigid bodies in 2D & 3D

Lecture 122 Work & energy principles for rigid bodies - intro 1

Lecture 123 Work & energy principles for rigid bodies - intro 2

Lecture 124 The rolling spool problem with & without friction - exercise

Lecture 125 The rolling spool problem with & without friction - solution 1

Lecture 126 The rolling spool problem with & without friction - solution 2

Lecture 127 The rotating ship problem - exercise

Lecture 128 The rotating ship problem - solution

Lecture 129 The torsion spring problem - exercise

Lecture 130 The torsion spring problem - solution

Lecture 131 The climbing rod problem - exercise

Lecture 132 The climbing rod problem - solution

Lecture 133 Lifting a post with a motor problem - exercise

Lecture 134 Lifting a post with a motor problem - solution

Lecture 135 Conservative forces & moments + potential energies - intro

Lecture 136 The rod and spring constant problem - exercise

Lecture 137 The rod and spring constant problem - solution

Lecture 138 The two gear and a cylinder problem - exercise

Lecture 139 The two gear and a cylinder problem - solution

Lecture 140 The disk, rod and collar problem - exercise

Lecture 141 The disk, rod and collar problem - solution 1

Lecture 142 The disk, rod and collar problem - solution 2

Lecture 143 Work & energy for rigid bodies in 3D - intro

Lecture 144 A 3D rotating sphere problem - exercise

Lecture 145 A 3D rotating sphere problem - solution 1

Lecture 146 A 3D rotating sphere problem - solution 2

Lecture 147 A 3D rotating satellite problem - exercise

Lecture 148 A 3D rotating satellite problem - solution

Section 6: Impulse & momentum for rigid bodies in 2D & 3D

Lecture 149 Impulse & momentum for rigid bodies - intro 1

Lecture 150 Impulse & momentum for rigid bodies - intro 2

Lecture 151 The space capsule problem - exercise

Lecture 152 The space capsule problem - solution

Lecture 153 The airplane yaw problem - exercise

Lecture 154 The airplane yaw problem - solution

Lecture 155 The rotating rod & disk problem - exercise

Lecture 156 The rotating rod & disk problem - solution

Lecture 157 The two cylinder and a pulley problem - exercise

Lecture 158 The two cylinder and a pulley problem - solution

Lecture 159 The spinning satellite problem - exercise

Lecture 160 The spinning satellite problem - solution

Lecture 161 The Hubble telescope rotation problem - exercise

Lecture 162 The Hubble telescope rotation problem - solution 1

Lecture 163 The Hubble telescope rotation problem - solution 2

Lecture 164 The hammer impact problem - exercise

Lecture 165 The hammer impact problem - solution 1

Lecture 166 The hammer impact problem - solution 2

Lecture 167 Impulse & momentum in 3D - intro

Lecture 168 The derivation of a simpler angular momentum formula - exercise

Lecture 169 The derivation of a simpler angular momentum formula - solution

Lecture 170 The rock and the space capsule problem - exercise

Lecture 171 The rock and the space capsule problem - solution

Lecture 172 The angular momentum of a satellite about a random point - exercise

Lecture 173 The angular momentum of a satellite about a random point - solution

Section 7: Newton VS Lagrange (Application to free undamped vibrations)

Lecture 174 Free undamped vibrations - intro 1

Lecture 175 Free undamped vibrations - intro 2

Lecture 176 Intro to application of the Lagrange method

Lecture 177 Pulley & block vibration problem - exercise

Lecture 178 Pulley & block vibration problem - solution 1

Lecture 179 Pulley & block vibration problem - solution 2

Lecture 180 Pulley & block vibration problem - solution 3

Lecture 181 Thank You!

Section 8: Last Words!

Lecture 182 Well done! You did it! But don't stop here! Keep going forward!

Engineering students in Control systems and in Mechanical, Civil, Aerospace, Maritime engineering,Professional engineers in Control Systems and in Mechanics, Civil, Aerospace, Maritime engineering