Domain

Explanation

What is dynamics?

• Phenomena, whether reality or virtual simulation, is composed fundamentally of changes
• Occurs on two scales:

1. Macro-scale: on & above the inter-atomic level (Newtonian & Relativistic realm) – relatively continuous
2. Micro-scale: on & below the atomic level, the quantum level (protons, neutrons, electrons, quacks) – relatively discrete

• All phenomena within these two scales are in unceasing motion – within & without the free body considered
• Energy, entropy, momentum & mass are totally conserved universally, but fluctuate on the global (macro) & local (micro) scales, resulting in various states
• For a considered free body, a resultant or imbalance of these universal components changes &/or disturb equilibrium state, giving rise to equilibrium states:

1. Stable: able to return to predefined undisturbed state
2. Neutral: equilibrium shifts to a new state
3. Unstable: unable for any equilibrium, undefined or unlimited equilibrium possibilities

• The aims of dynamics:

1. Identify phenomena – changing wrt. time, space & state
2. Representation – in the form of model for understanding
3. State response – attributes & properties culminating in behaviour
4. Analysis – reactions of model to applied changes like control, excitations or contamination
5. Applications – customization of reliable model to objectives like predictions, adaptation, monitoring and controlling

Dynamic modeling

• With appropriate assumptions to focus on investigation objectives, model (FBD) is constructed
• Identify influencing factors – external & internal
• Variables:

1. Definition
2. Range
3. Independent or Dependent

• From fundamental laws (energy, momentum, entropy & mass), derive mathematically the governing equation set
• Impose or set the model conditions:

1. BC: in space wrt. coordinate system
2. IC: in time wrt. temporal system

• Transformation into solvable form: PDE, ODE, state space
• Mathematical techniques:

1. Analytical solution: closed-form, theoretical, complex
2. Numerical approximation: weak-form, computational, iterative

• Analysis of results:

1. Solution verification towards model
2. Errors: truncation (consistency), convergence (model towards reality), round-off (stability realms)
3. Refinement: error reduction & mitigation
4. Understanding & insight into first, the model & then, the reality

Dynamic components

• Inclusive of all significant modeling parameters:

1. Basis components: distributed masses, damping, rigidity
2. Excitations: static, periodic, non-periodic, random
3. Measurement sensing: distributed gauging
4. Input controls: distributed controls by force &/or displacement
5. Modeling: response stability & control issues of observability (x(t) from u(t) & y(t)), controllability (transfer to x(t1) by t1) & stability (i.s.L., uniform/asymptotic stable, BIBO)
6. Disturbances: noises, delays, technical performance & lags