Dynamic Systems

Definition of Dynamic Systems

To understand the fundamental concept of systems, we first need to know what a system is. When studying something in physics, we want to consider exactly the things relevant to what we are studying and ignore everything else. The things we include in what we are studying are called our system. Plainly put,

We treat the objects in our system as if they had no internal structure. The internal structure of the objects should have no bearing on the final solution of the problem and can be ignored. Everything that is not part of our system is considered the environment.

A system can be a person and an automobile, a person and a skateboard, or even a classroom with desks and chairs. When calculating the acceleration of a system, we can use Newton's second law of motion. The properties and interactions of their substructures determine the properties of systems. When individual parts are not important for modeling the system's behavior, the system itself may be referred to as an object. According to Newton's first law of motion, only external forces affect a system's motion. That is because the law says an object at rest tends to stay at rest, and an object in motion tends to stay in motion. Since we have this distinction, defining the boundaries of a system should be done before we can understand what forces are affecting its motion.

For all systems and circumstances, energy, charge, linear momentum, and angular momentum are conserved except for an isolated or closed system, where conserved quantities are constant. We call an "interaction" a force caused by other objects outside the system, or the transfer of some quantity between the system and its environment. When solving a problem you consider the situation and make your own decision about the boundary between a system and its environment. The main characteristic of a dynamic system is a function that describes what future states follow from the current state.

What are the Basic Types of Systems?

There are three types of basic systems: Open, Closed, and Isolated systems. Below we will discuss some of the properties of each and how they relate to one another.

We start our discussion with open systems

Consider the following diagram of a heated flask. If our system is the beaker, then we have energy being added to the system in the form of heat, and matter leaving in the form of water vapor.

Model of an open system Wikicommons Public Domain

Closed systems are more restricted compared to open systems. Energy can still enter or leave the system, but now we add the restriction that matter cannot.

An example of a closed system Wikicommons, Public Domain.

Note that in a closed system you can have external forces, we just require that the net force on our system is zero.

Finally, we come to our most restricted type of system. Isolated systems, where, you may have guessed, we add a further restriction that both matter and energy cannot enter or leave the system. In practice, we cannot have a system that exchanges no energy with its environment, but it is still a useful tool for modeling some systems.

Example of isolated system Wikicommons Public Domain

An isolated system does not interact with its surroundings. Its total energy and mass stay constant.

Real-Life Examples of Systems

Dynamic Systems

Now let's take a look at what dynamic systems are.

Examples of Dynamic Systems

A dynamic system is a system where motion occurs, as opposed to static conditions with no motion. Dynamic systems are constantly moving or must change states to be useful.

Examples of Dynamic Systems include:

• Automobiles
• Computers
• A Swinging Pendulum
• Motions of Celestial Bodies

Dynamic Equilibrium System

Dynamic equilibrium in a reversible process happens when the forward and the reverse processes occur at the same exact rate thus, dynamic equilibrium is when all forces acting on an object are balanced.

There are three conditions to achieve equilibrium. First, the net external force of the system must be zero. Second, the sum of all external torques must be zero. Finally, we can say the object is in equilibrium when both conditions are met simultaneously. If one is not satisfied, the object is not in equilibrium.

• The equation is: $F\mathit{=}\mathit{0}$
• Static means motionless or stationary
• Dynamic means energetic

The system must maintain constant angular velocity and avoid accelerated rotation to achieve equilibrium.

Key Differences - Static and Dynamic Equilibrium

Static vs dynamic equilibrium chart StudySmarter Originals

Now that we can tell the difference between dynamic and static equilibrium, here are examples of dynamic equilibrium.

Discrete Dynamical Systems

Finally, we consider a specific type of dynamic system. In discrete dynamical systems, we consider the system in snapshots in time. Formally, we say:

These could be natural steps where things change at specific times. The United States government is one example of this. It is a system that evolves in time, but it does not change smoothly. There are specific points in time where changes occur. In this example, those points in time are elections. We can also artificially create discrete steps. Consider a census. The population data is updated every ten years. These are discrete steps, and we can make predictions and models based on this data, but the actual population change is far more continuous with people dying and being born every day.