例1-1如图所示,长方体边长b=2a,沿对角线AC1 作用一力F求该力在三个坐标轴上的投影
՟ བ᠔⼎ˈ䭓ᮍԧ䖍䭓 བ᠔⼎ˈ䭓ᮍԧ䖍䭓 ˈ⊓ᇍ㾦㒓 ⫼ϔ∖ 䆹ϝϾതᷛ䕈ϞⱘᡩᕅDŽ ⫼ϔ ∖䆹ϝϾതᷛ䕈ϞⱘᡩᕅDŽ r
解:采用二次投影法,有 F=-Fsin a cos B F= Fsin sin B F F=-F cosa B 代入AC1=√b2+a2=√a Ac 5a)+a sina=f, cosa=E, SinB=F, cosB=- 5 得 6,F- 16F 6F F F
㾷˖ 䞛⫼Ѡᡩᕅ⊩ˈ᳝ 䞛⫼Ѡᡩᕅ⊩ˈ᳝ α α β = − = = + = = − = = − = − α β = + = α = α = β = β = ҷܹᕫ
1-1-3力在坐标轴上的投影 2.合力投影定:汇交力系的合力在某轴上的投影等 于力系中诸力在同一轴上投影的代数和 设汇交力系(F,,…,F)的合力F和各分力的解析 表达式分别为 Fp=Fi FDj+ F k i= Fr i+ F j+Fik 代入式(1-3) F=F+E+…+F=∑F
ॉலဪቘު˖∛ѸLTDⱘড়ᶤ䕈Ϟⱘᡩᕅㄝ ѢLTDЁ䇌 ѢLTDЁ䇌ৠϔ䕈Ϟᡩᕅⱘҷ᭄DŽ ৠϔ䕈Ϟᡩᕅⱘҷ᭄DŽ r r r r = + + L r r r r = + + = r L r r 䆒∛Ѹ LTDⱘড় r ߚⱘ㾷ᵤ 㸼䖒ᓣ߿ߚЎ ॏၽᆵγᅀ౨ԅ ҷܹᓣ˄˅ r r r r r = + +⋅⋅⋅+ =∑
1-1-3力在坐标轴上的投影(续) 比较系数可得 ∑F ∑ F=∑F→F=∑F(10) ∑F→F2=∑
ॏၽᆵγᅀ౨ԅď༣ ॏၽᆵγᅀ౨ԅď༣Đ ↨䕗㋏᭄ৃᕫ = → = = → = = → = ∑ ∑ ∑ ∑ ∑ ∑ = = = ˄˅
1-1-3力在坐标轴上的投影(续) 而合力的大小和方向余弦分别为 F2=√(∑F)2+(ΣF)+F)2(1 COs(FR,i)=∑F/F cos(FR,j)=2F/FR (1-12) COS(FR,k)=∑F/F
ॏၽᆵγᅀ౨ԅď༣ ॏၽᆵγᅀ౨ԅď༣Đ = ∑ + ∑ + ∑ = ∑ = ∑ = ∑ r r r r r r 㗠ড়ⱘᇣᮍԭᓺ߿ߚЎ 㗠ড়ⱘᇣᮍԭᓺ߿ߚЎ ˄˅ ˄˅