Single Particle Dynamics | 1D and 2D Worked Examples

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Space Vehicle Dynamics, Lecture 7: Conservative forces (gravity and spring) 🔥 Single particle dynamics examples in 1 and 2 dimensions. 3D multiple frame kinematic example.

► Next: Kinetic energy: where does it come from? | linear momentum, angular momentum, and worked examples

► Previous, Rigid body dynamics overview | multiparticle system to continuous rigid mass distribution

Chapters
0:07 Conservative forces (forces from potential energy). Section 2.2 of Schaub and Junkins textbook (see below)
0:43 Newton's law of gravity
5:02 Spring, Hooke's law

Single particle dynamics
Section 2.3 of Schaub and Junkins book (see below)

7:03 1D examples of Newton’s Laws
7:19 no force
13:01 constant force
18:56 position-dependent force, simple harmonic oscillator

28:12 2D examples
28:28 Projectile motion
39:20 Pendulum equation of motion

53:57 3D multiple frame kinematic example

► More lectures posted regularly

► Dr. Shane Ross, aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA JPL and Boeing
Research website for @ProfessorRoss

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► Lecture notes (PDF)

► All course videos (playlist)

► Reference:
Schaub & Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018

- Typical reference frames in spacecraft dynamics
- Mission analysis basics: satellite geometry
- Kinematics of a single particle: rotating reference frames, transport theorem
- Dynamics of a single particle
- Multiparticle systems: kinematics and dynamics, definition of center of mass (c.o.m.)
- Multiparticle systems: motion decomposed into translational motion of c.o.m. and motion relative to the c.o.m.
- Multiparticle systems: imposing rigidity implies only motion relative to c.o.m. is rotation
- Rigid body: continuous mass systems and mass moments (total mass, c.o.m., moment of inertia tensor/matrix)
- Rigid body kinematics in 3D (rotation matrix and Euler angles)
- Rigid body dynamics; Newton's law for the translational motion and Euler’s rigid-body equations for the rotational motion
- Solving the Euler rotational differential equations of motion analytically in special cases
- Constants of motion: quantities conserved during motion, e.g., energy, momentum
- Visualization of a system’s motion
- Solving for motion computationally
- Other topics as time allows

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