1
Foundations — what a dynamic model is
2
Newton's method — single-DOF equations of motion
Topic 04
Newton's laws & free-body diagrams
The diagram that turns forces into an equation.
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Topic 05
The mass–spring–damper
The single most important equation in dynamics — and the live demo on the homepage.
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Topic 06
One pattern, many machines
The same second-order equation behind shafts and RLC circuits.
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Topic 07
The pendulum by Newton
A nonlinear oscillator, from forces and moments.
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Topic 08
Small-angle linearization
Turning a nonlinear model into one you can solve.
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Topic 09
Checking a model
Units, limits, and equilibrium — does the equation make sense?
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3
The energy / Lagrange method
Topic 10
Kinetic & potential energy
The energy bookkeeping behind the Lagrange method.
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Topic 11
Velocity from position
Differentiating coordinates to get the speeds energy needs.
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Topic 12
The Lagrangian & Lagrange's equation
One recipe that produces the equations of motion.
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Topic 13
Generalized forces & damping Q
Putting non-conservative effects into the energy method.
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Topic 14
Lagrange on one DOF
The spring and pendulum, redone the energy way.
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Topic 15
Coupled 2-DOF systems
Where the mass matrix first appears.
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4
Robot geometry — kinematics
Topic 16
Frames & the rotation matrix R(θ)
Describing orientation between coordinate frames.
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Topic 17
Homogeneous transforms & chaining
Position and orientation in one matrix, chained along a robot.
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Topic 18
Forward kinematics of the 2-link arm
From joint angles to end-effector position.
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Topic 19
Velocity kinematics & the Jacobian
How joint speeds map to end-effector velocity.
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Topic 20
DH parameters & 3-D
The standard convention for describing any robot. (Enrichment.)
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