Nhung phuong trinh chuyen dong potx

Nhung phuong trinh chuyen dong Toa do suy rong • Chat diem • Chat diem le mot vat the co kich thuok khong dang ke so voi quy dao chuyen dong • Bac tu do cua he • La dai luong doc lap can thiet xac dinh duy nhat mot vi tri cua mot he trong khong gian • Toa do suy rong • Ta thay rang khong phai luc nao viec xac dinh vi tri cua he bang cac toa do de cac cung thuan tien viec chon cac thong so can thiet de co dinh vi tri cua tat ca cac diem trong trong co he phai duoc xac dinh truoc het boi tinh hop li • S dai luong q1 q2… qsnao ham toan xac dinh vi tri cua he duoc goi la toa do suy rong cua he • Q1. q2. … qs .goi la toa do suy rong • Thuc nghiem chung to neu ta dong thoi cho toa do suy rong thi trang thai cua he se hoan toan xac dinh tren nguyen tac ta co the doan duoc chuyen dong tuong lai • He thuc lien he giua qi,qi.(i=1,s)dan den phuong trinh chuyen dong Nguyen li tac dung toi thieu (hamiton) Phat bieu nguyen li Theo nguyen li tac dung toi thieumoi mot co he duoc dac trung boi mot ham so L(q1 q2 q3 qs;q1. q2. q3. …qs.) hay L(q,q.,t)(phuong trinh lagrange) Chuyen dong cua he phai thoa man dieu kien :t=t1,t=t2he chiem nhung vi tri xac dinh duoc dac truong boi cac toa do suy rong q1,q2,thi giua 2 vi tri do he se chuyen dong sao cho s=tp l(q,q.,t)dt lay gia tri cuc tieu co the co cua no (ham tac dung cua co he) phat bieu dinh luatchuyen dong duoi hinh thuc cuc tieu cua ham skhong luon dung voi toan bo chuyen dong ma chi trong mot khoang kha be .Doi voi toan bo quy dao chuyen dong chi can co cuc tri khong nhat thiet phai co cuc tieu .Vi trong qua trinh lap luan ta chi dung den dieu kien cuc tri Phuong trinh lagrange Xet voi s=1 Gia su q=q(t)dung la ham so lam cho s cuc tieu q.=q(t)+&q(t) &q(t)<<q(t) &q(t0la bien thien cua ham q(t) &q tuy y ta co :pt L = $l/$q-d/dt.$l/$q. Neu biet ham l cua mot he thi pt so 2 se thiet lap duoc mot he thuc giua gia toc va,toc do va toa do , nghia la se thu duoc nhung phuong trinh chuyen dong Ve phoung dien toan hoc , n phuong trinh L lap thanh mot he s phuong trinh vi phan hang 2 ham so phai tim la qi Nghiem tong quat cua 1 he phuong trinh nhu vay se chua ham so do va dong thoi hoan toan xac dinh chuyen dong cua co he can phai cho biet cac dieu kien ban dau qi(i=1,s) va qi. • Tinh chat cua ham L • He gom 2 phan va B • Neu he a,b la he kin duoc dac trung boi La,Lb • Vay tai gioi han khi tach 2 phan do ra xa nhau den muc ma tuong tac cua chung bo qua thi: • LimL=La+Lb • Xet 2 ham L • L(q,q.,t);L’(q,q.,t);2 ham L nay khac nhau 1 dao ham toan p’han phu thuoc vao toa do thoi gian • L’(q,q’;t)=L(q;q’;t)+d/dtf(q,t) • S’=tpL’(q,q’,t),dt,t1,t2=tpL(q,q’,t)t1,t2+tpd/dtf(q,t)dtt1,t2=tpt1,t2L(q,q’,t)+f(q,t),t1,t2 • &S’=&S+F(q,t),t1,t2=&s • Chu y:phan biet giua vi phan (d) va bien thien (s) • Bien thien lien quan den chuyen quy dao nay sang quy dao khac • Vi phan lien quan den su bien doi chuyen dong quy dao doc theo quy dao • Trong k/n bien thien &q ta co 2 ham Q(t),q(t)nhung chi lay mot gia tri cua bien ,con trong vi phan ta chi co mot ham q lay 2 gia tri khac cua bien so t Nguyen li tuong doi Ga li le • He quy chieu quan tinhkhac , • Trong nhung he quy chieu quan tinh khac nhau ‘nhung dinh luat chuyen dong noi chung se co dang khac .neu chon mot he quy chieu tuy y thi co the xay ra nhung dinh luatcua nhung hien tuong don gian se tro nen rat phuc tap trong he quy chieu do .vi vay xay ra mot la tim duoc 1 he quy chieu sao cho trong he do xay ra nhung dinh luat co hoc don gian nhat • Doi voi he quy chieu bat ky ,khong gian khong dong chat va khong dang huong • 1 vat bi co lap thi nhung vi tri khac nhung phuong huong khac cua no trong khong gianse khong tuong duong voi nhau ve phuong dien co hoc • Cung tuong tu nhu vay doi voi thoi gian se khong dang huong ,nghia la nhung thoi diem la khong tuong duong voi nhau • Nguoi ta nhan thay rang luon co the tim duoc 1 he quy chieu sao cho khong gian la dong nhat va dang huong , thoi gian la dong nhat , he quy chieu nhu vay duoc goi la he quy chieu quan tinh • Dang cua ham l cua ham chat diem tu do trong mot he quan tinh • Tinh dong chat cua khong gian,L khong chua ro vecto r • Tinh dong chat cua thoi gian L khong chua ro t • L phu thuoc vao vec to v • Tinh ddang huong cua khong gian L khong phu thuoc vao huong cua v • Trong mot he quan tinh mo chuyen dong tu do se xay ra toc do khong doi ke ka phuong va huong • Nguyen li tuong doi Ga li le • Neu canh mot he quy chieu quan tinh san co ta dua vao mot he quy chieu quan tinh khacchuyen dong thang deu doi voi he quy chieu quan tinh do thi nhung dinh luat tu do thi doi voi he quy chieu cung doc lap voi he quy chieu ban dau cac dinh luat co hoc se xay ra doi voi he quy chieu quan tinh • Cac dinh luat co hoc deu xay ra nhu nhau trong moi he quy chieu quan tinh . thu duoc nhung phuong trinh chuyen dong Ve phoung dien toan hoc , n phuong trinh L lap thanh mot he s phuong trinh vi phan hang 2 ham so phai tim la qi Nghiem tong quat cua 1 he phuong trinh nhu. L(q,q.,t) (phuong trinh lagrange) Chuyen dong cua he phai thoa man dieu kien :t=t1,t=t2he chiem nhung vi tri xac dinh duoc dac truong boi cac toa do suy rong q1,q2,thi giua 2 vi tri do he se chuyen dong. Nhung phuong trinh chuyen dong Toa do suy rong • Chat diem • Chat diem le mot vat the co kich thuok khong dang ke so voi quy dao chuyen dong • Bac tu do cua he • La