more math (coalesce notes)

m₁v₁ + m₂v₂ = m₁v_1f + m₂v_2f

m₁v_1f = m₁v₁ + m₂v₂ - m₂v_2f

m₁v_1f = m₁v₁ + m₂(v₂ - v_2f)

• v_1f = (m₁v₁ + m₂(v₂ - v_2f)) / m₁ Then solve for v_2f in the other equation & substitute? where exactly does the cosΘ come from? I’d have to figure that out, anyways, and I’m not 100% sure how. (Hell, I don’t have a clue.) m₁v₁² + m₂v₂² / 2 = … wait … why the x/2? Both sides of the equation are divided by 2. Couldn’t I just get rid of it? The answer to that, of course, is yes. but basically I’m solving for 4 unknowns. 2 vectors = 2 sets of 2 values each. Either force + angle or dx + dy. And I can convert between those. m₁v₁² + m₂v₂² / 2 = m₁v_1f² / 2 + m₂v_2f² m₁(v₁² - v_1f²) = m₂(v₂² - v_2f²) m₁(v₁² - v_1f²) / m₂ = v₂² - v_2f² v_2f² = v₂² - m₁(v₁² - v_1f²) / m₂

So I should treat all collisions (that don’t destroy both objects) as collisions between spherical objects, at least as far as determining the post-collision movement vectors. Then I need to determine the line connecting their centers, and calculate the objects’ movement vectors (x,y components) relative to that line. The y component will remain unchanged. [some notes pertaining to a graph that won’t make sense w/o the image] v_1f =

• v₁ + m₂(v₂ - (v₂² - m₁(v₁² - v_1f²) / m₂))) / m₁ [sic]
• v₁ + m₂(v₂ - (v₂² - (m₁v₁² - m₁v_1f²) / m₂)) / m₁
• v₁ + m₂v₂ - m₂(v₂² - (m₁v₁² - m₁v_1f²) / m₂) / m₁
• v₁ + m₂v₂ - (m₂v₂² + m₁v₁² - m₁v_1f²) / m₁
• v₁ + m₂v₂ - m₂v₂² / m₁ + v₁² - v_1f²
• v_1f + v_1f² = v₁ + m₂v₂ - m₂v₂² / m₁ + v₁²
• [this next equation looks wrong]

this doesn’t help me! a² + b² = c² ? (Do I know either a or b? I don’t think I do.) This can’t be that hard. Hell, if it helps I can even tweak the equation so one body is at “rest”. I need a good geometry / physics book. But I can’t. I’m already behind on my bills. There’s the internet, granted, but that’s not the same. [many more trig. notes that would be useless w/o the diagrams accompanying]