The Concept of a Particle, a Rigid Body, and a Deformable Body 

When we observe the real world around us, we see objects such as cars, buses, trains, ships, apples, aircraft, buildings, and various kinds of machines. In contrast, when we look into the literature on classical physics which aims to help us understand, and sometimes even predict and control, the behavior of these objects, we encounter concepts such as particles, rigid bodies, and deformable bodies. 

So, what are these so-called particles rigid bodies and deformable bodies?

How are they different from each other?

What is the relationship of these concepts and the real-world objects?

I welcome you to this blog post, where I will answer these questions in detail.

In the engineering or scientific analysis of a real-world situation using the principles of classical physics, we begin by simplifying the problem through a set of assumptions or idealizations. These assumptions allow us to replace the real system with a simplified version that retains only the essential features needed to achieve the goals of the analysis. This simplified representation is commonly referred to as an idealized model, or simply a model, in the engineering and scientific community.

Once a model of the real system is obtained, the laws of physics are applied to derive the equations governing its behavior. This set of equations is known as the mathematical model of the problem. The mathematical model relates the parameters and variables that describe the behavior of the simplified system. These governing equations can be solved either analytically (which is quite rare) or numerically, in order to understand, predict, or even control the behavior of the system under consideration. The solution of these mathematical models using numerical methods on a computer is referred to as numerical simulation.

Particles, rigid bodies, deformable bodies are different models used for the analysis of real-world objects. 

In particular-

Particle:
Model of an object where the size and shape are neglected, and all its mass is assumed to be concentrated at a single point. Only  translational motion is possible.

Rigid body:
Model of an object in which the distances between all points of the body remain constant during motion, meaning deformation is neglected while both translational and rotational motions are allowed.

Deformable body:
Model of an object where shape and size can change under the action of forces, so that internal deformations and stress–strain relationships must be considered.

The same object can be modeled as a particle, rigid body, or a deformable body depending on the purpose of analyzing that object. Let us take several concrete examples to illustrate this idea more clearly.

Example 1: A person throwing a potato

Consider a person throwing a potato through the air. Depending on what we want to know, we ask different questions — and each question requires a different level of modeling.

How far does the potato land?

What matters:

·         Initial speed

·         Launch angle

·         Gravity

·         (Optionally) air resistance

What does not matter (at first):

·         Exact shape of the potato

·         How it rotates

·         Whether it deforms slightly in flight

Appropriate model: Particle

Here, the potato can be modeled as a particle, possibly even without explicitly worrying about its mass. We track only the motion of its center of mass. This is sufficient because the question is purely about the trajectory.

Key idea: When only the gross motion is of interest, internal structure is irrelevant.

At what angle does the potato land?

What matters now:

·         Orientation of the potato

·         Rotation during flight

·         Angular velocity and angular momentum

What is still negligible:

·         Deformation during flight (if the potato is stiff enough)

Appropriate model: Rigid body

To answer this question, the potato must be treated as a rigid body. Unlike a particle, a rigid body has:

·         a finite size,

·         a shape,

·         and an orientation that evolves with time.

The landing angle depends on how the potato rotates as it moves, which cannot be captured by a particle model.

Key idea: When orientation and rotation matter, the object must have extent.

Will the potato burst on hitting the ground?

What matters:

·         Material properties of the potato

·         Internal stresses and strains

·         Rate of impact

·         Energy dissipation

Appropriate model: Deformable body

Here, the potato must be modeled as a deformable body, because bursting depends on how the material:

·         compresses,

·         cracks,

·         and possibly fails.

Neither particle nor rigid body models can describe internal stress or damage.

Key idea: Failure and damage are inherently deformation-driven phenomena.

Example 2: An airplane flying

Consider an airplane flying through the air. Depending on what we want to analyze, different questions arise, and each question naturally leads to a different modeling assumption.

What is the gross path followed by the airplane?

What matters:

·         Position of the airplane

·         Velocity and acceleration

·         External forces such as gravity and thrust

What does not matter:

·         Exact shape and size of the airplane

·         Orientation of the wings

·         Structural details

Appropriate model: Particle

If we are interested only in the overall trajectory of the airplane, it can be modeled as a particle. The airplane is treated as a point with a certain mass, and only the motion of its center of mass is tracked. It does not matter whether the rear end of the plane lags slightly behind the nose, or how wide the wings are, because such details do not influence the gross path.

Key idea: When only translational motion is of interest, the object can be idealized as a particle.

Is the airplane stable during a turn or maneuver?

What matters:

·         Size and shape of the airplane

·         Orientation in space

·         Rotational motion

·         Distribution of mass

What is still neglected:

·         Structural deformation of the airplane

Appropriate model: Rigid body

To study stability, rotation, and maneuvering, the airplane must be modeled as a rigid body. In this model, the airplane has a fixed shape and size, and its orientation and angular motion are explicitly considered. This allows us to analyze moments, angular momentum, and forces acting on the wings and fuselage, while assuming that the structure remains undeformed.

Key idea: When orientation and rotation matter, the object must be treated as a rigid body.

How do the wings and fuselage deform under aerodynamic loads?

What matters:

·         Material properties

·         Stress and strain distribution

·         Bending and twisting of wings

·         Vibrations and fatigue

Appropriate model: Deformable body

If the goal is to analyze structural stresses, vibrations, or wing flex during turbulence, the airplane must be modeled as a deformable body. In this case, different parts of the airplane are allowed to bend, twist, and stretch under aerodynamic and inertial loads. Such modeling is essential for ensuring structural safety, predicting fatigue, and designing lightweight yet robust aircraft structures.

Key idea: Structural response and failure require deformable body models.

Choosing the right simplification ensures that the analysis is efficient while still producing meaningful results. 

So, I think now you clearly know what are particles, rigid bodies, and deformable bodies? How they differ from each other? and What is their relationship with the real world objects? 

Thanks for reading.