Apparent Mass in massive and massless particles in dynamics:

Soumendra Nath Thakur
March 20, 2025

In ECM Force equation of massive particle expressed as:

Fₘₐₛₛ = (Mᴍ + (-Mᵃᵖᵖ))aᵉᶠᶠ

In ECM Force equation of massless particle:

Fₘₐₛₛₗₑₛₛ = (-Mᵉᶠᶠ + (-Mᵃᵖᵖ))aᵉᶠᶠ, 

where: Mᴍ = -Mᵉᶠᶠ, since Mᴍ < 0 also, Eg can be equated as -Mᵉᶠᶠ = E𝑔 and E can be equated as: -Mᵃᵖᵖ = E

Simplified as:

Fₘₐₛₛₗₑₛₛ = (-Mᵃᵖᵖ + (-Mᵃᵖᵖ))aᵉᶠᶠ where -Mᵃᵖᵖ = -Mᵉᶠᶠ, since Mᴍ <0  = - Mᵉᶠᶠ 

Further Simplified:

Fₘₐₛₛₗₑₛₛ = (-Mᵃᵖᵖ + -Mᵃᵖᵖ))aᵉᶠᶠ where E𝑔 can be equated as -Mᵉᶠᶠ = E𝑔 and E can be equated as: -Mᵃᵖᵖ = E

Resolved as: 

Fₘₐₛₛₗₑₛₛ = -2·Mᵃᵖᵖ·aᵉᶠᶠ