Summary of Extended Classical Mechanics: Vol-1 (Rev-2,3)

21 November 2024

This paper explores how classical mechanics can be extended to account for modern scientific concepts like dark matter, dark energy, and negative mass. It focuses on how these concepts affect the understanding of mass and gravitational dynamics.

Key Points:

Equivalence Principle Redefined: The traditional equivalence principle (inertial mass = gravitational mass) is re-examined to include dark matter.

• Matter Mass (Mᴍ): This represents the combined mass of normal (baryonic) matter and dark matter.
• Apparent Mass (Mᵃᵖᵖ): This is a negative mass component introduced to account for situations involving motion and strong gravitational fields. It influences the Effective Mass (Mᵉᶠᶠ), which is the sum of matter mass and negative apparent mass.
• Gravitating Mass (Mɢ): This is the total effective mass of a system, incorporating both matter mass and negative apparent mass. It is equivalent to the mechanical effective mass (Mᵉᶠᶠ).
• Dark Energy and Negative Mass: Dark energy is reinterpreted as a negative apparent mass term, influencing gravitational dynamics.

Modifications to Existing Equations:

• Newton's Second Law is modified to include effective mass and effective acceleration.
• Newton's Law of Universal Gravitation is reinterpreted to account for effective mass.

Methodology:

• Reinterpreting existing concepts in light of extended classical mechanics.
• Developing mathematical models to quantify the relationships between different mass components and their impact on gravitational interactions.
• Analysing how the interplay of mass components affects gravitational forces and dynamics.
• Using simulations to test the models and compare with observational data.

Expected Outcomes:

• Refine the understanding of mass dynamics in extended classical mechanics.
• Explore the implications of negative apparent mass for gravitational theories.
• Gain insights into the role of dark energy and its interaction with matter.

Overall, this research proposes an extended framework for classical mechanics that incorporates modern scientific understanding of mass and gravity.

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