The NKTg Law on Varying Inertia

Introduction

The NKTg Law on Varying Inertia is a proposed physical principle that describes how an object's tendency to move in space depends on the interaction between its position, velocity, and mass. Unlike Newtonian mechanics, which assumes mass is constant, this law incorporates the possibility of variable mass and its effect on motion.

General Equation

The law can be expressed generally as:

$NKTg=f(x,v,m)$

Where:

$x$ is the position or displacement of the object relative to a reference point.
$v$ is the velocity.
$m$ is the mass, which may vary with time.

Fundamental Quantities

Two core quantities describe the motion tendency:

$NKTg_{1}=x\times p$
$NKTg_{2}={\frac {dm}{dt}}\times p$

Where:

$p=m\times v$ is the linear momentum.
${\frac {dm}{dt}}$ is the rate of change of mass over time.
NKTg₁ is the product of position and momentum.
NKTg₂ is the product of mass variation and momentum.

The unit for both quantities is NKTm, representing a unit of varying inertia.

Interpretation

The values and signs of $NKTg_{1}$ and $NKTg_{2}$ indicate the motion tendency:

If $NKTg_{1}>0$ : the object tends to move away from the stable state.
If $NKTg_{1}<0$ : the object tends to move toward the stable state.
If $NKTg_{2}>0$ : mass variation supports the motion (positive contribution).
If $NKTg_{2}<0$ : mass variation resists the motion (negative contribution).

Definition of Stable State

A stable state is defined as the condition where position, velocity, and mass interact harmoniously to maintain the motion structure of an object. This helps the object preserve its inherent movement pattern and avoid uncontrolled motion.

Applications

Potential applications of the NKTg Law include:

Astrodynamics — where spacecraft experience mass loss due to fuel consumption.
Particle physics — involving variable-mass particles or decaying systems.
Mechanical systems — with components that change mass during operation.

By accounting for mass variation, the NKTg Law extends classical mechanics to a broader class of dynamic systems.

Author

This proposed physical law was introduced by independent researcher Nguyễn Khánh Tùng.

Open-access publications:

User:Nguyennhuhuyen/The NKTg Law on Varying Inertia