Source Of Complexity

Lesson

Introduction
Matter of scale
Variability
Non-linearity
Introduction to differential equations
Governing equations
- Introduction
- Balance of mass and Linear Momentum
- Balance of Moment of Momentum
- First law of thermodynamics
- Second law of thermodynamics
Different approaches
Exercises
To go further
Conclusion

Balance of mass and Linear Momentum

The balance of mass is a fundamental law is physics and chemistry, it shows that during the evolution of the system, the mass is preserved, but also that the number of each chemical species of elements is conserved.

$\begin{equation*} \frac{dM_v}{dt} = 0 \end{equation*}$

M Denotes the total mass within a volume V , So the conservation of mass reads : The mass of a material body does not change.

The linear momentum is the first dynamical law that enables us to write down equations describing the motion of a body. It corresponds to Newton's second law (1687) : The time rate of change of the momentum of a body equals the sum of all external forces that are acting on this body.

$\begin{equation*} \frac{dP_v}{dt} = K_{\partial V} + K_V \end{equation*}$