Analytical mechanics

Analytical mechanics is a way to understand how things move and why they move the way they do. It helps us study how objects move in different conditions like in space or on Earth.

To understand analytical mechanics, let's first think about how we move a toy car. When we push the car with our hand, it moves forward. We can also move the car backwards by pushing it the opposite way. This is because of a force that we apply to the car. Everything that moves, moves because of a force.

Analytical mechanics looks at how forces interact with objects, and how these interactions cause things to move or not move. This is called mechanics. And it is called analytical because it uses mathematical formulas to describe the movements.

For example, if we wanted to figure out how fast a toy car would go if we pushed it really hard, we can use a formula to calculate its speed. This formula takes into account the car's mass, the force we applied to it, and the distance we pushed it.

Analytical mechanics also studies how different forces affect an object's motion. For example, if we throw a ball in the air, we can see that it moves up and then comes back down. This is because of two forces - gravity and air resistance. Gravity pulls the ball down while air resistance slows it down.

Analytical mechanics helps us to understand how these forces relate to each other and affect the object’s motion.

In conclusion, analytical mechanics is a way to study how forces affect the motion of objects through math formulas. It helps us understand why things move and how different forces interact with each other.